Hi Greg,
Body-weight exercises are great for increasing strength. Make sure to target all muscles so you do not get muscle imbalances.
Try out pushups, reverse rows, dips, pull ups, chin ups, handstands, etc.
For abdominals do planks, dead bugs, side planks, crunches, oblique crunches, and supermans.
Squats and lunges will strengthen the gluteus maximus, the quadriceps femoris and the soleus but they don't target the hamstrings. A good one for hamstrings is a Swiss Ball Hamstring Curl.