Moira’s damage orb is going to be one of the primary sources of ultimate charge during your games. You should aim to cast it in high traffic areas at the start of a game, or before a fight when the enemies aren’t close.
If the enemy has an Ana on her own, you can sneak up on her and use a damage orb with biotic grasp to quickly kill her. Before doing this, make sure she has used at least one of her cooldowns. After doing this, you can fade into the fight with your team and cast coalescence to quickly capture the point if needed.
D.Va can be annoying to go against when playing Moira, especially if she focuses eating your orbs with defence matrix. Try to get your team to prioritise destroying her meka suit so you can cast more damage orbs freely. Once D.Va is out of her meka, Moira should be the one to try and finish her off since it’s a lot easier for her to hit D.Va. As soon as she ejects you should throw a damage orb through her and in the path of another enemy.