What strength training exercises can I do without lifting weights to tone up and lose weight?

There are options. You could do isometric exercises. This means that you use your own body to create resistance. Imagine pushing against a door that is already locked, this generates muscle contraction but you aren't lifting anything heavy. Also aqua aerobics is a good option. You will have resistance from the water but again you don't have to lift anything heavy. Talk to your primary doctor to get their blessing.