Other people seem to know the specifics far better than I do but here's what springs to mind:
Amp - he uses a Vox AC30. He also has a Roland Jazz Chorus - I guess he hasn't really used it since the Enz days but he is seen using it on the Rock Arena New Year's concert filmed at the end of '86. He said that he found the JC to have a hollow sound that bugged him. I think it sounds great. I have no idea but I always assume that the lovely sound of the guitar on Recurring Dream is, in part, courtesy of the JC. I think he used to use the distortion switch on at almost its lowest. That way the guitar wasn't always ridiculously clean (E.g. that open A-ish chord at the end of the middle-8s on One Step Ahead). Again, I'm not as technically wise as others here are so maybe they'll correct me on that.
Accoustics - he uses Maton. I think he uses a junior sized one. Not sure of the exact model. He probably has a couple.
Pedals/Effects - in the Enz days I think his sole pedals were a MXR Flanger and a Paul Crowther Hot Cakes distortion pedal. The Hot Cakes is awesome - you can get one from Paul Crowther direct if you like. Can't remember now where I got the address and details from but they must be out there somewhere. Great pedal.
He used to use a Roland Tape Echo unit but that got the chop at the end of the Enz days. You can hear it in all its glory on the guitar echos on One Mouth. I have one somewhere - kind of funky but such a big piece of equipment. As many people say, the warmth of it IS nicer than digital but I don't think its size is practical for the road. I grew to really resent lugging that thing around! God knows if you can still get tapes for it too.
In the mid/late 80's he bought a Yamaha SPX unit I think. I'd doubt he's still using that though. No real idea what his effects setup is right now but I'd be willing to bet that the Hot Cakes is still in it.