Sonic the hedgehog (Archie) is all but banned in the Battles forum because of how overpowered he is (especially when the chaos emeralds (or chaos force) are in the mix). Game Sonic has weaknesses and limits due to the mechanics which the comics lack. However, while a lot of creative liberties are taken, the comics draw heavily from the games (coming out with special issues whenever sega makes a new main series game).
Ambiguous in power, straight out stated to be faster than light in the early stories. Actually lacks a direct connection to the chaos force that Knuckles and Shadow share in this continuity. He also seems to be a wild card (dubbed as merely being another champion) in the ancient prophecies which focus on Knuckles (the avatar: Chaos Knuckles) and Tails (the chosen one: Titan Tails). Despite this, he still bares the title of being the fastest "thing alive" on his planet.
One or more chaos emeralds allow him to use Chao Control (time manipulation and teleportation). But like his game counter-part he prefers not to use it.
Same as the game (collect 50 or more rings once 7 or more chaos emeralds have been collected). Abilities are the same as the games (nigh-invulnerability, increased speed, chaos abilities, and flight) without game mechanic limits (being smashed and drowning won't kill him in this form). Only other chaos based entities seem to effect him. However Archie Sonic has been able to transform without rings and from different chaos based power sources. One super emerald (a power source which we'll get to later), and the master emerald. Super Sonic always seems to be on equal footing with characters that are supposed to be "stronger" due to them having a direct connection to the chaos force. Like Chaos Knuckles (the Avatar of the ancient echidna prophecy) or Enerjak (another echidna entity). Best feat comes from when he and knuckles in his super form (Hyper Knuckles, knuckles' counter-part to Super Sonic) destroyed a zone (dimension) while fighting inside of it.
Ultra Sonic and The Super Emeralds:
As was mention previously, one Super Emerald can facilitate a tranformation into Super Sonic yet it also can transform him into Ultra Sonic. Ultra Sonic doesn't change Sonic's appearance like Super Sonic does. It grants him the ability to manipulate and transmute matter, adapt to different climates (solar Sonic in heat, polar Sonic in cold, eco Sonic in a forest), fly, and create portals to other dimensions.When Sonic first transformed he used one super emerald and "a lot" of rings. The second time he used one super emerald while running as fast as he could (this is also when he used the adapted forms). The last time he used it he just gathered a lot of rings and transformed on his own (no emeralds). The Super emeralds are based on the items that debuted in Sonic 3 and Knuckles. When Sonic collected 7 of those Super Emeralds he became Hyper Sonic (in the games Knuckles collected chaos emeralds to become Super Knuckles and Super emeralds to become Hyper Knuckles; whereas in the comics Hyper Knuckles is the name for "Super" Knuckles). Fan speculate that if Sonic collected 7 Super Emeralds Archie Hyper Sonic will be invincible; though while this is unsubstantiated, we can assume that an archie Hyper Sonic could share the abilities of Super Sonic and Ultra Sonic. Hyper Sonic in the game was faster than Super Sonic, wasn't able to drown (game mechanic weakness), and had a "hyper/chaos flash" ability which killed all non-boss enemies on the screen. A super emerald also mutated Sonic into his modern design (green eyes, longer spikes etc.)
Hyper Sonic (game only)