You have to complete the following goals to unlock the corresponding bonuses. Then, you can easily enable them at the weapons or game options screens:
Worms bleed when shot: get gold medal in Basic Training mode
Aqua sheep: get gold medal in Super Sheep Racing training mode
Longbow power-up: get gold medal in Euthanasia training mode
Shotgun power-up: get gold medal in Rifle Range training mode
Grenade power-up: get gold medal in Artillery Range training mode
All weapon crates have sheep: get gold medal in Crazy Crates training mode
Invincibility: get an Elite rank in Deathmatch mode
Laser sight: accomplish mission 4
Jetpack: accomplish mission 8
Fast walk: accomplish mission 13
Invisibility in net games: accomplish mission 16
Low gravity: accomplish mission 20
Indestructible landscape: accomplish mission 25
Super Banana Bomb power-up: accomplish mission 33
Full Wormage game options: get Gold medal and Elite rank in all