I have not battled competitively in a while, but thought that I might try and get back into it. So... Here goes.
Ferrothorn @ Leftovers
Ability: Iron Barbs
Nature: Relaxed (+ Def, - Sp)
Evs: 252 HP / 208 Def / 48 SpD
-Spikes
-Leech Seed
-Power Whip
-Gyro Ball
Ferrothorn is the team's Physical Wall. Its job is to set up Spikes. Leech Seed allows it to recover. Power Whip and Gyro Ball are for STAB, and they also provide good coverage. Ferrothorn works well with Starmie, because they have good defensive coverage. Ferrothorn is very afraid of anything using Fire type attacks, so whenever something that usually packs Flamethrower comes out, it needs to run. In this scenario, I would switch out to Haxorus or Starmie to save it. In summary, Ferrothorn lays down entry hazards and blocks any leading sweepers.
Haxorus @ Life Orb
Ability: Mold Breaker
Nature: Adamant (+ Atk, - SpA)
EVs: 252 Atk / 4 Def / 252 Spe
-Dragon Dance
-Taunt
-Earthquake
-Outrage
With already huge attack, after a few Dragon Dances, Haxorus becomes a serious threat. Taunt shuts down Skarmory, the only one who walls this set completely. Outrage is the powerful STAB move. Earthquake, with Mold Breaker, allows Haxorus to hit Pokemon with Levitate. This set is partially inspired by the Gyarados set I ran in Generation 4. Whenever a scarfed Dragon such as Garchomp switches in, unless Haxorus has been able to DD several times, it must run. In this case, I would switch in Starmie or Ferrothorn. All in all, Haxorus makes a powerful Physical presence.
Eelektross @ Expert Belt
Ability: Levitate
Nature: Rash (+ SpA, - SpD)
Evs: 252 Atk / 212 SpA / 4 Spe
-Wild Charge
-Flamethrower
-Grass Knot
-Brick Break
Eelektross is the team's Mixed Attacker. Wild Charge is for STAB and a powerful electric move. Flamethrower takes care of Ferrothorn and other Grass types. Grass Knot removes the threat of bulky water and ground types. Brick Break, in addition to the other moves, provides for excellent coverage. Although Electivire is arguably a better mixed sweeper, it does not have the access to Grass Knot that Eelektross does. In addition, Eelektross' lack of weaknesses thanks to Levitate means that doesn't have to fear much, except maybe an opponent's Haxorus, in which case I would switch it out for Starmie.
Jellicent @ Leftovers
Ability: Cursed Body
Nature: Bold (+Def, -Atk)
Evs: 252 HP / 212 Def / 44 Spe
-Scald
-Recover
-Hex
-Psychic
Jellicent functions as the team's spin blocker. Psychic hopefully removes the awful fighting weakness. Even though Water Absorb might be preferable over Cursed Body in some circumstances, Cursed Body allows Jellicent to shut down Choice Pokemon. Scald provides primary STAB and has the added bonus of potentially burning the foe, which helps the team survive longer. Hex is for secondary STAB and will do even more damage thanks to Drapion's Toxic Spikes and Scald. With Recover, Jellicent can survive much longer. All in all, a great spin blocker and a great addition to the team.
Heatran @ Air Balloon
Ability: Flash Fire
Nature: Modest (+ SpA, - Atk)
Evs: 4 HP / 252 SpA / 252 Spe
-Fire Blast
-Earth Power
-Dragon Pulse
-Substitute
Heatran replaces Starmie as the team's primary Special Sweeper. Air Balloon temporarily negates ground attacks, so Heatran can avoid Earthquake until it takes a hit. Modest nature is a given, giving it plenty of attacking power. Fire Blast destroys anything that does not resist it. Earth Power helps Heatran hit Pokemon that resist Fire Blast. Dragon Pulse covers Dragons that would Earthquake Heatran into dust. Finally, with Substitute, Heatran can protect itself further.
Drapion @ Leftovers
Ability: Battle Armor
Nature: Careful (+ SpD, - SpA)
Evs: 252 HP / 4 Def / 252 SpD
-Toxic Spikes
-Whirlwind
-Crunch
-Earthquake
Drapion can lay down two layers of Toxic Spikes easily. Crunch provides it with a decent STAB move that helps Drapion beat Ghosts and Psychics. Earthquake kills Steel and Poison types, both of which oppose Toxic Spikes. Whirlwind allows Drapion to poison the enemy's team, and also hurts them with the Spikes laid down by Ferrothorn. This double threat weakens the team's enemies to the point that Haxorus or Eelektross can easily finish them off. Drapion is shut down by Skarmory or anything with Taunt. Skarmory switching in requires Drapion to switch to Eelektross.
Starmie @ Leftovers
Ability: Natural Cure
Nature: Timid (+ Spe, -Atk)
Evs: 4 Hp / 252 SpA / 252 Spe
-Rapid Spin
-Surf
-Ice Beam
-Recover
Starmie functions as my Rapid Spinner. Timid with max speed Evs allows it to remove entry hazards that would cripple the rest of the team. Surf is for STAB. Ice Beam removes Dragons that cause problems for Haxorus. Recover and Leftovers keep Starmie around a little longer. Spin Blockers don't threaten Starmie much, except for Jellicent, because of it's great Special Attack. Bulky Water types like Suicune are able to stop Starmie from doing much. When they switch in, Starmie needs to switch out to Eelektross.
Bisharp @ Air Balloon
Ability: Defiant
Nature: Adamant (+ Atk, - SpA)
Evs: 132 HP / 172 Atk / 204 SpD
-Pursuit
-Sucker Punch
-Iron Head
-Thunder Wave
Bisharp is the revenge killer and status inducer. It can get rid of Ghost types that threaten Starmie. Iron Head is for STAB. Thunder Wave stops enemy sweepers. Sucker Punch provides priority STAB. Pursuit gives Bisharp another STAB move and lets it hit anything trying to run. Balloon allows Bisharp to avoid Earthquake temporarily, and thus allows it to remain on the field longer. Bisharp complements Haxorus, as it cleans up anything that survives the Dragon type's rampage. Thus, Bisharp's job is to annoy the opponent and to finish off anything the other team members don't.
Sword and Shield
For this team, I decided to go in a different direction than I have in the past. Rather than just using Spikes for the entry hazard, I have also incorporated Toxic Spikes. In addition, thanks to Starmie, I now have a Rapid Spinner. All in all, this team should be more effective than what I have used in the past.
The name of the team is inspired in part by Haxorus' blade-like tusks. Appropriately, Haxorus is the physical sweeper, and thus functions in a similarly to a sword. The shield represents both Ferrothorn and Drapion.
As far as threats, this team is pretty weak to Fighting moves, however, thanks to Jellicent, that problem is at least partially resolved.
The name of the team is inspired in part by Haxorus' blade-like tusks. Appropriately, Haxorus is the physical sweeper, and thus functions in a similarly to a sword. The shield represents both Ferrothorn and Drapion.
As far as threats, this team is pretty weak to Fighting moves, however, thanks to Jellicent, that problem is at least partially resolved.
Ferrothorn @ Leftovers
Ability: Iron Barbs
Nature: Relaxed (+ Def, - Sp)
Evs: 252 HP / 208 Def / 48 SpD
-Spikes
-Leech Seed
-Power Whip
-Gyro Ball
Ferrothorn is the team's Physical Wall. Its job is to set up Spikes. Leech Seed allows it to recover. Power Whip and Gyro Ball are for STAB, and they also provide good coverage. Ferrothorn works well with Starmie, because they have good defensive coverage. Ferrothorn is very afraid of anything using Fire type attacks, so whenever something that usually packs Flamethrower comes out, it needs to run. In this scenario, I would switch out to Haxorus or Starmie to save it. In summary, Ferrothorn lays down entry hazards and blocks any leading sweepers.
Ability: Mold Breaker
Nature: Adamant (+ Atk, - SpA)
EVs: 252 Atk / 4 Def / 252 Spe
-Dragon Dance
-Taunt
-Earthquake
-Outrage
With already huge attack, after a few Dragon Dances, Haxorus becomes a serious threat. Taunt shuts down Skarmory, the only one who walls this set completely. Outrage is the powerful STAB move. Earthquake, with Mold Breaker, allows Haxorus to hit Pokemon with Levitate. This set is partially inspired by the Gyarados set I ran in Generation 4. Whenever a scarfed Dragon such as Garchomp switches in, unless Haxorus has been able to DD several times, it must run. In this case, I would switch in Starmie or Ferrothorn. All in all, Haxorus makes a powerful Physical presence.
Eelektross @ Expert Belt
Ability: Levitate
Nature: Rash (+ SpA, - SpD)
Evs: 252 Atk / 212 SpA / 4 Spe
-Wild Charge
-Flamethrower
-Grass Knot
-Brick Break
Eelektross is the team's Mixed Attacker. Wild Charge is for STAB and a powerful electric move. Flamethrower takes care of Ferrothorn and other Grass types. Grass Knot removes the threat of bulky water and ground types. Brick Break, in addition to the other moves, provides for excellent coverage. Although Electivire is arguably a better mixed sweeper, it does not have the access to Grass Knot that Eelektross does. In addition, Eelektross' lack of weaknesses thanks to Levitate means that doesn't have to fear much, except maybe an opponent's Haxorus, in which case I would switch it out for Starmie.
Jellicent @ Leftovers
Ability: Cursed Body
Nature: Bold (+Def, -Atk)
Evs: 252 HP / 212 Def / 44 Spe
-Scald
-Recover
-Hex
-Psychic
Jellicent functions as the team's spin blocker. Psychic hopefully removes the awful fighting weakness. Even though Water Absorb might be preferable over Cursed Body in some circumstances, Cursed Body allows Jellicent to shut down Choice Pokemon. Scald provides primary STAB and has the added bonus of potentially burning the foe, which helps the team survive longer. Hex is for secondary STAB and will do even more damage thanks to Drapion's Toxic Spikes and Scald. With Recover, Jellicent can survive much longer. All in all, a great spin blocker and a great addition to the team.
Heatran @ Air Balloon
Ability: Flash Fire
Nature: Modest (+ SpA, - Atk)
Evs: 4 HP / 252 SpA / 252 Spe
-Fire Blast
-Earth Power
-Dragon Pulse
-Substitute
Heatran replaces Starmie as the team's primary Special Sweeper. Air Balloon temporarily negates ground attacks, so Heatran can avoid Earthquake until it takes a hit. Modest nature is a given, giving it plenty of attacking power. Fire Blast destroys anything that does not resist it. Earth Power helps Heatran hit Pokemon that resist Fire Blast. Dragon Pulse covers Dragons that would Earthquake Heatran into dust. Finally, with Substitute, Heatran can protect itself further.
Drapion @ Leftovers
Ability: Battle Armor
Nature: Careful (+ SpD, - SpA)
Evs: 252 HP / 4 Def / 252 SpD
-Toxic Spikes
-Whirlwind
-Crunch
-Earthquake
Drapion can lay down two layers of Toxic Spikes easily. Crunch provides it with a decent STAB move that helps Drapion beat Ghosts and Psychics. Earthquake kills Steel and Poison types, both of which oppose Toxic Spikes. Whirlwind allows Drapion to poison the enemy's team, and also hurts them with the Spikes laid down by Ferrothorn. This double threat weakens the team's enemies to the point that Haxorus or Eelektross can easily finish them off. Drapion is shut down by Skarmory or anything with Taunt. Skarmory switching in requires Drapion to switch to Eelektross.
Previous team members:
Starmie @ Leftovers
Ability: Natural Cure
Nature: Timid (+ Spe, -Atk)
Evs: 4 Hp / 252 SpA / 252 Spe
-Rapid Spin
-Surf
-Ice Beam
-Recover
Starmie functions as my Rapid Spinner. Timid with max speed Evs allows it to remove entry hazards that would cripple the rest of the team. Surf is for STAB. Ice Beam removes Dragons that cause problems for Haxorus. Recover and Leftovers keep Starmie around a little longer. Spin Blockers don't threaten Starmie much, except for Jellicent, because of it's great Special Attack. Bulky Water types like Suicune are able to stop Starmie from doing much. When they switch in, Starmie needs to switch out to Eelektross.
Bisharp @ Air Balloon
Ability: Defiant
Nature: Adamant (+ Atk, - SpA)
Evs: 132 HP / 172 Atk / 204 SpD
-Pursuit
-Sucker Punch
-Iron Head
-Thunder Wave
Bisharp is the revenge killer and status inducer. It can get rid of Ghost types that threaten Starmie. Iron Head is for STAB. Thunder Wave stops enemy sweepers. Sucker Punch provides priority STAB. Pursuit gives Bisharp another STAB move and lets it hit anything trying to run. Balloon allows Bisharp to avoid Earthquake temporarily, and thus allows it to remain on the field longer. Bisharp complements Haxorus, as it cleans up anything that survives the Dragon type's rampage. Thus, Bisharp's job is to annoy the opponent and to finish off anything the other team members don't.
So, that's it. Thanks to Chillarmy for the suggestions.
(Sets inspired by those found on Smogon)