오다 and 가다 has difference by your position standards.
오다 is used when a person move to where you are. Also, it can be used when you or other person who are in same place(this is can be you) go out and come back the place.
And 가다 is used when a person (or you)move to the place far from where you are in now. So it can be used when you move to another place.
So, saying again, moving to where you are or moving from where you are.
So 데리고오다 is used when someone picked up other person and go to where you are. On the contrary, 데리고가다 is used when you or someone picked up others and go to other place.
데려가다 and 데려오다 is shorten words of aboves.