уносить to take something away from a place
относить to take something away from its current place and bring it to another one
приносить to bring something to a new place after having taking it from its old place
нести to carry something that is in your hands or as a burden

to make the difference between the words perfectly clear, let me provide an example:

Imagine a house with rooms, but only two of them are interesting to us, the first is a kitchen, and the other is a bedroom. There are three people in the house. The first is Jack, the second is Lidia, the third is Jerry.

Jack and Lidia are in the kitchen. Jerry is in the bedroom.

Lidia asked Jack to take an apple to the bedroom. So he took it and started moving towards the bedroom with it . From the point of Lidia's view Jack относит the apple, but from Jerry's point of view Jack приносит the apple. But, for Lidia Jack уносит the apple as well. However if Lidia didn't know where Jack took the apple to she could only say that Jack уносит the apple

For both Lidia and Jerry Jack несёт the apple because he moves holding the apple in his hands. (If he put the apple in a pocket, or in a backpack or in a purse or something similar, he'd still perform the носить action)

I hope this helps