use your own weight. Also if you can afford dumbells that helps.
For your legs, you can do one legged squats. Builds both strength and balance. And squatting using only one leg is the equivalent of squatting with a fair amount of weight. Lunges also can be done without weights. Adding dumbells to either exercise will increase the intensity.
For upper body, dips and chin ups are good exercises. Dips can be done with the aid of a chair. Chin ups, you'd need to mount a bar. And of course there are pushups.
Stability ball gives you lots of core work out options.
another option are exercises using a stretch cord.
For $100 in dumbells, stability ball, stretch cord, and maybe a book or two, you'll have everything you need to work out at home, and only a small amount of stuff to stick under the bed or in the closet.