Am sure the Tom who is good at offwidths will be along soon to offer some better advice but in the meantime...
I had a fun few months a few years ago really getting into climbing offwidths and I learned a few things (NB I only got to about E1/2 level).
Firstly, offwidth climbing is a lot more technical than I'd assumed. I thought if you rock up, get (literally) stuck in and give it the proverbial 110% I'd be good. Not so.
You need to get used to the fact that that style of climbing is really a constant trade off between being comfortably (ish) wedged in a crack, but unable to move, or unwedging yourself and falling out/off.
The technical element is to know how much friction to sacrifice to unwedge yourself enough to shuffle/move upward, but without falling off totally.
There is also loads to learn about various arm/leg wedging techniques, but if you've seen or follow The Wideboyz you'll know your chicken wing from your salmon tickler.
Reading offwidths is a bit of an art (which way to face, do you turn round?), as is trad gear management, unless you have a huge rack of big cams.
Buy some big cams. They make life immeasurably easier. Also some cheap long sleeve tops. Skinned backs of triceps really sting.
Best advice I can give you is just do loads. Me and my mate started out as total punters but after a month or so got vaguely proficient.
We spent most of our time at Brimham, which has arguably the best concentration of offwidths of all grades. There's even an offwidth boulder problem!
If you are in or around Yorkshire the "Dirty Dozen" list in the green guide is a good start. There's also an alternative dozen as a ticklist on UKC.
As for non climbing training, not much I can recommend. It's a very physical style of climbing, and uses whole of body grunt so a shitload of bodyweight deadlifts would probably help in terms of general fitness.
Hope that all helps!
