If the only long-distance train rides you will take are Nagoya to Osaka and Kyoto to Tokyo, then the 7-day JR pass probably will not "pay off." From Kyoto to Tokyo possibly take a nighttime highway bus and save on one night's lodging. If you're really on a tight budget, it might be the least-cost solution.
However, try to think more broadly about the JR pass before dismissing it outright on a "tickets vs. pass" cost basis. Among other things, having a JR pass will let you economically "commute" from any lodging near a JR station to anywhere within reasonable day trip distance. (And what is a "reasonable" day trip could change based on many factors, including whether it's raining in Kansai but not an hour or two away by fast train.) The JR pass can also be used on short-distance JR transit. If you want, you can build an entire itinerary, including local sightseeing, around the pass. There is no reason why you have to follow the usual approach of setting up a fixed sightseeing agenda (for example, "top ten" sites in Kyoto/Osaka), with no regard for which train lines serve the places you want to go, and then paying with an IC card (at no discount). There are so many wonderful places to see in Kyoto, Osaka, and Tokyo (and within an hour or two by JR from these cities) that you can pick ones that are accessible by JR and have a fabulous trip using a JR pass strategically. (Or if you really MUST go to tourist magnets that are not reachable by JR, make strategic use of non-JR passes. It's a total myth that none of the day passes in Kyoto pay off, for example. You just have to devote a lot of time to figuring them out and planning your routes.)
Here's a little-known fact that can save you money on lodging: there has been a huge hotel building boom in Kyoto in the last five years, and there are now so many rooms in the lower and middle budget range that the vacancy rate on weekdays during non-busy seasons is staggering. Hundreds and hundreds of rooms are available in late May and early June, for example. Kyoto has become a bargain bonanza if you go at the right time, especially if you can avoid Saturdays. The prevailing wisdom these days is that Kyoto is completely inundated with tourists and is just ridiculously crowded and expensive. Well, during cherry blossom season and fall foliage season, that is true. However, at other times, and if you avoid the major tourist magnet sites, lodging there can be surprisingly cheap (of course, you do have to shop--but it's a lot easier than in Tokyo or even Osaka).
So think broadly about your money-saving, and at least consider getting a JR pass. If you can save say 1000 (or more) a night for five nights staying in Kyoto over some other city that doesn't have dozens of brand new hotels (and guest houses and hostels) competing viciously, and you pick sightseeing venues that are on JR so you can use the pass to get to them (saving maybe another 500 or so yen per day), it could offset the cost of the pass enough that it's actually cheaper than the typical approach.
Just something to think about. In the end, when you go and where you stay will probably be bigger cost considerations than whether you get a JR pass or not. But you need to be prepared to do a lot of research on your own, to reap the rewards. It sounds like you are at the beginning of your planning. Nobody here is going to figure everything out for you, but you can get specific questions answered as you go along. Just keep working at it and you'll get there eventually.