Can you transfer between States in the National Guard if State TA was used?

That applies to the Cadet in their situation because they're under contract with the state to pay their tuition in exchange for later service as a commissioned officer. For enlisted, we incur no service obligation using TA, whether it's Active, National Guard, or Reserves.

Great question, you CAN transfer even if you used state TA. You can put in a hardship request to let you ranger. The issue comes in of you had a GI bill kicker or an enlistment bonus. You'd have to pay those back, but they'll still let you transfer.

No, National Guard State Tuition assistance for enlisted does not come with an additional state service obligation, it part of the package to entice you to enlist. If and when you decide to transfer out of state, you need to contact the State Headquarters of your new location, most will have someone that deals with out of state transfers and should help you find a new home. Then you will still need to get a Condition Release (DD368) signed off by the first General in your COC. Your gaining unit should help you get that paper work ready for signature, but you will need to get it to your COC.
If you have remaining enlistment bonus money, you can kiss that goodbye. The contract I most often saw gave 1/3 on MOS qualifications, 1/3 at two years and 1/3 at four years. If you have taken that last one, they may want part of it back for the unserved time in state.
You will here some nightmare stories about State to State transfers, but I will say that I moved several times during my Guard years and didn't find it a major hassle at all.
It's been a few years since I as Active Guard, but the rules haven't changed much. Run into a specific question, just let me know.