Use the classic song "Head, Shoulders, Knees and Toes" (see Resources) as your starting point. Use the same rhythm but substitute the words for whichever bit of anatomy you are learning. Try to keep things in some sort of logical order, such as working down the body. For example, if you are learning the bones of the leg you could sing "Femur, patella, tibia, fibula. Tibia, fibula and talus and calcaneus and metatarsus and phalanges. Fembur, patella, tibia, fibula." Point to each part of the body as you name it to help you remember its position. You can extend this to any system in the body, though you might need to say some names a bit quickly to make them fit to the rhythm.
Take a well-known song, such as "Jingle Bells," and rewrite the lyrics to describe a system or part of the body. If possible, make some of the last words in the lines of your rewrite rhyme with the last words of lines in the orginal. For example, change "Dashing through the snow, in a one-horse open sleigh, o're the fields we go, laughing all the way" to "Through the heart the blood does flow, passing the lungs on its way, right atrium right ventricle, and through left side the other way". This can require a pretty hefty investment of time to get the songs written, but once done they'll stick in your head for years.
Play clapping and song games in a group using questions and answers to test each other on anatomy. For example, sit in a circle and clap all together in time, twice on the knees and twice with the hands. The first person then thinks of a muscle or bone and calls out two bones or two muscles that connect to it. The person to his right has the time of two hand claps and two knee claps to remember which bone or muscle connects to the two the person on the left named. If he gets it correct, he then has two more knee and hand claps to think of his own question to ask to the person on his right. You can speed up the rhythm gradually to make the game more intense.