Took me a while of messing around with the file KeyMapCustomController, before I could play the game with this controller. In case anyone else wants to play New 'n' Tasty with the Strike controller, I thought I'd share it. Save the following as KeyMapCustomController.cfg in the Settings folder (you'll also need to set your controller to analog):

Interact=JoystickButton3,None
Crouch=JoystickButton1,None
Jump=JoystickButton2,None
Sneak=JoystickButton4,None
Shoot=JoystickButton3,JoystickButton2
Beat=JoystickButton1,None
Throw=JoystickButton6,None
BirdHalo=JoystickButton0,None
Chant=JoystickButton5,None
AltGamespeak=JoystickButton7,None
Run=JoystickButton5,None
Pause=JoystickButton9,None
Quiksave=JoystickButton8,None
MenuAccept=JoystickButton2,None
MenuBack=JoystickButton1,None
MenuDelete=JoystickButton3,None
LeaderboardChangeRanking=JoystickButton1,None
LeaderboardChangeDifficulty=JoystickButton0,None
LeaderboardChangeCategoryLeft=JoystickButton4,None
LeaderboardChangeCategoryRight=JoystickButton6,None
MenuHorizontal=JoystickAxis1,None,False
MenuVertical=JoystickAxis2,None,True
MovementHorizontal=JoystickAxis1,None,False
MovementVertical=JoystickAxis2,None,True
ThrowingHorizontal=JoystickAxis3,None,False
ThrowingVertical=JoystickAxis5,None,False
GamespeakHorizontal=JoystickAxis6,None,False
GamespeakVertical=JoystickAxis7,None,False