You may be able to swim—it depends on the injury, but swimming with a pool buoy between your knees may work because it restricts your movements to the upper body.
You can also try upper-body weight lifting or using an upper-body ergometer (a machine that looks like a bike for your arms). Core strengthening may be doable too, and even Pilates—tell the instructor you might modify moves. (Hit the reset button—and burn fat like crazy with The Body Clock Diet!)
As for your uninjured leg, don’t worry about strength training it alone—it will be getting enough exercise from all the extra work it’s doing to compensate for the hurt leg.