I am afraid this looks like it could be a costly exercise. Your parter can file for divorce in either the state of Nevada or Ohio. That's the easy bit. So too is the process of commencing the action. You would still require the services of an Attorney however, and probably a solicitor from the UK too.
But what complicates your partners case is that he is not resident in either state, and both states have a residency requirement where the party filing for divorce must be resident in the state for a period of 6 weeks before beginning the divorce action.
So it seems that the solution is move to Ohio or Nevada or, more logically, your partner should try to make contact with his wife and ask her to divorce him (perhaps at his expense)? He may wish to write to the company she works for leaving his contact details so he can be contacted on a personal matter. It's either that or use a private detective to make contact.
I don't think it would even help to take an extended holiday since I think that would fall short of what would be required to constitute what being 'resident' is - suggesting a degree of permanency.
http://www.leg.state.nv.us/NRS/NRS-125.html#NR S125Sec010 (Check the first two sections - NRS 125.020 -section 2).
http://codes.ohio.gov/orc/3105 - (see 3105.62).