How to connect the MTH TIU which is stationary to movable layout which using star wiring

 You could use banana plugs wired to the layouts star wiring and when the layouts lowered just plug them into the TIU. 

 If you are using more than one channel of the TIU and 16 gauge wiring will do the trick. I would look into automotive trailer plugs. Long pigtails to connect to the layouts wiring and the TIU. Connector that only plugs together one way with multiple color wires.

I would use banana plugs.  If you use more than one TIU channel, use electrical tape or heat shrink tube to color code the wires.

I think the banana plugs are a good idea as well. Here are some from Digikey 461-1214-ND that I have been happy with. They fit tightly in the banana jacks and don't come loose. I have tried a couple of other brands with out much success, these are still working well after a couple of years.

If you used the MTH terminal blocks on the layout you could unplug at either end you wanted to, or even both ends.