My friend made me an Ent race and it is a large creature. If he gave it racial ability score mods would those add to the +16 to strength, +8 to con, and -4 to dex from size?
Ability score adjustments due to a change in size category occur only when the creature changes size
When a creature increases or decreases its current size category via magic or advancing Hit Dice or another method, that is when the modifiers to the creature's statistics from the Creature Size table apply, unless the method's description says otherwise or provides different modifiers (and many do).
Otherwise, for example, the DM would have to adjust the statistics of every storm giant to account for the creature's Huge size.