Will jogging help strengthen my knees and ankles??

Well, running puts a lot of stress on your joints. Whether it is good or bad for them depends on how your body responds to this stress. In general when a part of your body is stressed (bone, joints, muscles, even to some extent the brain) it responds by repairing itself stronger than it was before. However, if you stress the body beyond its ability to repair itself than instead of getting stronger it gets weaker.

For most people who already have bad knees and ankles the stress of running is too much and leads to problems. For other people the stress may strengthen their joints.

I ran in high school but as I got older my joints could no longer handle the strain of running. I tried tennis and had similar issues though my orthopedic surgeon thinks I can play tennis if I loose weight and don’t overdo it.

If you have a problem with your knees or ankles, whatever program of exercise you choose should be of medium intensity. Jogging would be too hard impact. You could walk or ride a bicycle or swim for your cardio. But if you want to strengthen your joints maybe you should take up something like yoga and also consider taking supplements that are joint-specific.

No. Jogging will damage your knees and ankles. To strengthen them, you need to walk, not jog.