Rulebook page 20-21:

RELICS
Certain immobile objects are listed as a “Relic.” A relic will be listed with a range of numbers. Relics can’t be destroyed. If a character occupies the same square as a relic, that character may be given a power action to roll a d6 that can’t be rerolled. This roll is called a relic roll. If the result of hat roll is within the indicated range of numbers (or higher), the relic is assigned to that character, placed on that character’s card, and the character will gain certain abilities, as described on the relic’s card. When a character with a relic on their character card is defeated, place the relic in the square they last occupied. At the end of the game, if an opponent’s character has a relic on their card or all of your characters have been defeated, victory points for the relic are scored by your opponent.

If an opponent has a character that picked up a relic or assigned a relic...say a hammer hits AM will he get the +1 or +2 from his trait since he got hit with an object since relics are considered as an object.

If so....will the hammer be removed from the opponent and be placed on his card?

He will get nothing. In a case ase you describe, he is not hit with an object. He is just hit by a guy who has an object assigned to him.

To clarify, his trait takes effect when a character uses an object as a weapon to attack "Uru Man." This is either using an object as a striking weapon with Super Strength, throwing it with Super Strength, Telekinesis, or flinging an Ultra-Light object.