Overview:
Uh...not sure where to start. Basically, a phrase that describes Arceus is "Jack of all trades, master of all." Basically, Arceus can do almost anything, but unlike others who are also versatile, Arceus can actually do things well. With the possibility to be any type, a massive movepool, and base 120 stats across the board, I don't think it's a joke to say Arceus is the most powerful Pokemon in the game. The only possible weakness to Arceus is that it can't do everything at once, but then again, it doesn't need to because it is that strong. Or that non-Normal type Arceus can't use any other Hold Item except the plate it needs, but even that doesn't really take away from Arceus' amazing epicness.
Abilities:
Multitype: When Arceus holds a "Plate" item, its type changes to match the type of plate it is holding. This is what makes Arceus truly scary, as it can be any one of the 17 (soon to be 18 (assuming that release a plate for Fairy)) types, giving Arceus the pinnacle of versatility in the game.
Sets:
Honestly, due to the sheer number of sets that could be done, I'll stick with one that has been posted already (because it's AMAZING!) and try and come up with something by myself.
Extreme Killer
-Swords Dance
-Extremespeed
-Shadow Claw
-Earthquake/Brick Break/Recover
Item: Life Orb/Leftovers
Ability: Multitype
Arceus' Type: Normal
Nature: Adamant (+Attack, - Sp. Attack)
EVs: 88 HP, 252 Attack, 168 Speed
This is one of the greatest sets ever. I've used it quite a bit, and it is awesome. Basically, use Swords Dance to boost your Attack by 2 stages and slaughter. What makes this set so epic is the Same-Type-Attack-Bonus (STAB) that Arceus gets from Extremespeed, since in this form, Arceus is a Normal-type and Extremespeed is as well. Because Extremespeed has +2 Speed priority, the only way for a Pokemon to strike Arceus first would to be faster than Arceus AND have Extremespeed. Yikes. Shadow Claw, Earthquake, and Brick Break are all coverage moves against Ghost, Rock, and Steel types that wall Extremespeed. Yeah, it's crazy.
The item choice comes down to even more power at the cost of 10% of Arceus' max HP every time it hits (Life Orb) or gaining back 1/16 of its max HP every turn (Leftovers). Life Orb is usually preferred just to kill stuff even more effectively, but the option is there. Adamant nature and 252 Attack EVs max out Attack, while the Speed EVs allow Arceus' Extremespeed to outrun Rayquaza's Extremespeed, with the rest in HP.
Arceus, the Great Wall
-Calm Mind
-Judgement
-Recover
-Will-o-Wisp/Roar/Thunder
Item: Iron Plate
Ability: Multitype
Arceus' Type: Steel
Nature: Bold (+ Defense, -Attack)
EVs: 248 HP, 252 Defense, 8 Sp. Attack
This set is similar to one of Arceus-Steel's sets, but a bit different. Basically, using the best defensive type in the game, this Arceus is very tough to take down. Calm Mind boosts Arceus' Sp. Attack and Sp. Defense by one stage each, which is good for both offense and defense (especially his "weaker" defense in this set). Judgement is a powerful move, though the offensive coverage is a bit lacking, but with so much power behind it, who cares? Recover restores Arceus' HP, making it even more difficult to take down. Will-o-Wisp inflicts "Burn" status, which also cuts the target's Attack in half as a result, allowing for even greater survivability. Roar phases out opponents such as boosting sweepers and Pokemon that are slightly more difficult to handle. Thunder should only be used if Arceus is paired with Kyogre, as Drizzle causing the weather to be Rain makes Thunder have perfect accuracy.
While a Timid (+Speed, -Attack) nature could be done on this set, I think the Bold nature is a nice twist to make Arceus have even more Defense, thus harder to take down. The EVs max out physical bulk.
Other Options:
...Other Plates. We'll just leave it at that.
Checks and Counters:
I don't think there is a good "universal counter" to Arceus, seeing as it can be any type and run many sets as each type. Honestly, it's going to depend on what set/type Arceus is, and even then, the checks and counters are still going to be a bit hard-pressed due to Arceus' amazing stats and movepool. Basically, Arceus is a Pokemon that will cause issues for you if you're up against it.