At the beginning of each combat, creatures you control gain first strike until end of turn if a creature you control has first strike. The same is true for flying, deathtouch, double strike, haste, hexproof, indestructible, lifelink, menace, reach, skulk, trample, and vigilance.
Odric’s ability triggers at the beginning of each combat, not just combat on your turn, whether or not any creatures you control have any of the listed abilities. If a creature gains one of the listed abilities before Odric’s triggered ability resolves, perhaps due to another ability that triggered at the beginning of combat, then creatures you control will gain that ability.
The set of creatures affected by Odric’s ability and how they are affected is determined as the ability resolves. Creatures you begin to control later in the turn won’t gain any abilities or cause creatures to gain new abilities, and the abilities gained won’t change even if every creature that normally had the abilities leaves the battlefield.
Multiple instances of any of the abilities Odric can grant your creatures are redundant.