No, there are no weapon size rules in 5e beyond Heavy weapons being off limits to size Small races. There is no feature like that in the Elemental Evil Players Companion entry for the Goliath race.

Can a Goliath one hand a greatsword?

The answer is no, because: A goliath is a medium creature. Using a medium-size greatsword requires two hands for medium creatures.

Are Goliaths considered large?

The goliath sense of fairness, balanced with an emphasis on self-sufficiency and personal accountability, pushes them toward neutrality. Size. Goliaths are between 7 and 8 feet tall and weigh between 280 and 340 pounds. Your size is Medium.