If you really want to lose weight and can't do cardio, eat clean. I wouldn't neccesarily do a low cal diet since all they do is make you hungry, and once you start eating normal again you tend to gain more than you took off. If I were you, I would cut out sugar, pop, salt, fatty meats, etc. and load up on veggies, whole wheat products, fruit, lean meats and plenty of water. I have gotten terrific results when I eat this way. I injured my foot a few years ago and couldn't do anything, but I ate very clean and looked as tone as I did when I was working out and actually lost fat. OH, and I was NEVER hungry. You get hungry because your body needs food and nutrients, so don't ignore that symptom! Just make sure you treat your bod with what it needs.
Lifting weights will boost your metabolism, and is part of the equation that equals fatloss. (BTW, I actually find that when I lift weights my appetite does increase as well as when I do cardio. Just make sure that you are eating well.) I haven't ever done a rotation that did not include cardio, and the only people I know who do it are men, but they are completely different from us, and some of the female personal trainers, but they are kind of butch and definately not sending the same message that I want to, so if I did stregth, it would be a low weight high rep workout.
There are those that are far wiser than I who hopefully will post as well, especially about the strength training!
Missy