As stated elsewhere, I am 53 and new to weight training in the past few weeks. My goals are not only to tone, but to protect my bones. I am not yet menopausal.

I have read in numerous publications that squats and lunges are valuable exercises...but when I do them, I do feel knee strain. Also, I guess because my thigh muscles are tight despite doing yoga, I can't easily do proper form and even sometimes lose my balance doing lunges when I come back upright. Any suggestions for alternative exercises which will give the same benefit as squats and lunges?

Have you tried ball squats? (Ball against wall, squat down?)

Also, you can do lunges on a step (front foot on step) or for balance work on a bosu.

I have osteoarthritis in my knee and I just don't go too deep on the squats, do what is comfortable, etc. Same for lunges.

Where is your knee going when you are doing those squats and lunges.

I was having a LOT of knee problems with these exercises due to bad form...my knee was traveling forward during the exercises, pushing it out over my toes. That is a recipe for knee pain. Once I adjusted my form so that my knee always stayed directly over my ankle (basically, keeping my lower leg/calf perfectly perpendicular to the ground), I had way fewer problems. You should only be going down so far that you can maintain that form...otherwise, you're just hurting your knees and not really working the muscles you are trying to work.

Try squats against a wall/with a ball if you're still having issues after adjusting for form.

It really takes a while to correctly perform a squat. An extra set of eyes is helpful too. In addition to not letting the knee go past the toe, keep the weight in your heels and not allow it to shift forward.

Ideally, I should be able to place my fingers under the toes of your shoe and you wouldn't step on them with much weight during the phases of the squat. When coming back up, make sure again that you use glute strength to push back up. The glutes are recruited more effectively when you are settling into your heels.

Lunges were more difficult for me to master than squats. I do have osteoarthritis under my knees. I found that backward lunges were easier first then I could begin to lunge forward. It took me a little time to build the quad and hamstring strength as well as core strength in stability to execute the move. Just practice. You'll get it.

If you have arthritis or a known knee injury you may consider doing prone jackknifes or hamstring curls on the swiss ball. Not a complete substitute but a good thing to have in your rotation if you are experiencing knee pain on a particular day.

You could try isometric wall sits where you have your back against the wall and slide down til you're sitting (like in an invisible chair) and just hold it for time. Start at 30 secs and increase it as you get stronger.

With squats and lunges you can hold onto something-the back of a chair, a dowel rod, anything that's about waist level for a little extra stability.
Step ups are also a good alternative.

Good luck

edit:
Oh, I forgot about hamstring bridges. I hold 3 positions for 1 minute each: feet in line with knees, knees together and feet apart, and feet together and knees apart.