Does the power token on characters improve their STR or does they simlpy prevent taking thems in power chalenge?

power on characters still count towards your win total and cannot be stolen by a power challenge, but does not inheirantly provide a strength bonus.

Generally speaking, the primary benefit of Power on a character is that it cannot be stolen during a Power Challenge. The primary weakness is that it will be lost if the character dies.

That said, there are cards (most notably from Brotherhood) that benefit in other ways when there is Power on a Character instead of on your House Card.