How hard would you have to pull on iud strings to move it out of place? would the strings feel longer if that happened ?

IUD movement: IUDs are normally quite stable though small movements are possible. A small change of string length with no pain is usually fine. A large change of length or pain mandates a follow-up with the person who put it in.

IUD: You would probably feel it being pulled through your cervix and it would be very uncomfortable and the string would certainly be longer