What is a good calisthenics routine to build strength (not mass)?
Push ups with varying hand widths and hand positions such as fingers pointing in, out and back. Try using your finger tips and then just the thumb and forefinger of each hand as you progress. Everyone talks about planks. Try one armed push ups. Take a match. Put it in your mouth. Do a one handed push up. On the down side place the match between the thumb and forefinger of the hand that is on the ground. Go down and remove the match with your mouth. Push up. Go down and place the match between your forefinger and middle finger. Go up. Complete the cycle until the match is between your little finger and the finger next to it. Reverse the cycle ending with the match in your mouth.
Sit ups, twisting sit ups and leg raises.
Inverted wall press ups. Note the word press. Get your body more vertical than in a wall push up.
Dips can be done using a sturdy pair of chairs.
Chin ups and pull ups. Varying hand widths from wide to close as well as some behind the neck.
Body weight squats, pistol squats and one legged calf raises using a stair to get the stretch in your calves. When you can do 10 pistol squats in succession with each leg you have strong legs and a strong core that maintains your balance.
To work your back in the opposite movement of sit ups and leg raises some yoga moves such as the cobra, to bridges to the bow and finally the wheel.
A long time ago, in another century, the pistol squats were a martial arts exercise that I believe have been made popular by the cross fitters. Another martial arts exercise that may interest you might be a flexibility exercise. Stand erect. Spread your legs apart. Fold your arms placing each hand on top of the other arm's forearm. Now try to touch your elbows to the floor. That will keep your hamstrings stretched out. It makes a toe touch with the palms flat on the floor child's play.
All exercises should be done with a full range of motion.