The Onslaught perk gives a 20% boost to
- all damage dealt (melee, ranged, splash, spell/nukes)
- movement speed
Picking Onslaught perk also prevents the player from taking Iron Man mastery during the game. The only way to get Iron Man Mastery with Onslaught is by also taking the Tenacity perk, which provides Iron Man Mastery at the start of the game and a 20% health boost to all units.
The Onslaught perk does not apply to your minions or any units under your control.