When I have need to rent clubs I have always done so at the course I was playing but I have not played any course on Oahu. The only option that I can really think of is to call (or check websites) of places like Golfsmith, Golf Galaxy etc to see if they have a location and rent clubs. Also, a smaller more local golf shop might rent clubs so I might check the yellow pages and give a few a call.
As far as places to play I can't help much there either (ask about the Big Island and I can help) but I know that almost all resorts allow outside play so finding a place to play won't be a problem. The cost however might be a factor. I know on the Big Island the places I typically play have a discounted rate after 100PM so you might consider that to make a resort course more affordable.