Lift up that corner of the car and support it with a t-stand then with the wheel still on,... grab it at the 12 and 6 o-clock position and give it a firm shake/wobble/shimmy,.. at different "rpms" until you hear the clunk. Don't rotate the tire ,... try to twist it (pulling at the top of the tire while pushing at the bottom then vice versa).
Try to get a helper to shake the wheel while you look for movement (the axle doesn't really count,... it's kinda "free floating" as mentioned above (unless it's really worn out)).
I'm betting on the ball joints,... my car did the same sort of thing.
You can also use a pinch bar/chisel/wrench handle/big flat head screw driver and reef between the control arm and steering knuckle (right beside the ball joint) to check for movement (as well as other spots to check for movement).
The ball joint is under quite a bit of pressure and needs a pinch bar to show the slack (worn ball joints easily throw off your steering wheel and make steering sloppy,.. and scrub out your tires too,... check your tread for feathering on the edges,.. your alignment can go way off with worn ball joints).
You may have worn out steering linkages instead,.. similar sloppy steering,.. you'll be able to see that slop too,... grab the tire at the 9 and 3 positions for that test, it shows steering slop,... the key is to leave the tire on and reef like hell,... there's a lot of heavy friction you need to overcome to show the slack.