If I place a barrier in front of a character on an outdoor map can giants and larger or characters on elevated terrain shoot over the barrier?

They can shoot over to hit any other elevated figures (If the barrier is on level 1, they can target level 2) Beware, they can reach over and punch those right on the other side.

So a colassal on the same elevation as the barrier can shoot over it and hit the characters behind it?

A on Lv 1drawing a Line of Fire to a character on Lv1 which crosses a square of Blocking Terrain on Lv 1 will have LoF blocked.

A on Lv 1 drawing LoF across a square of Blocking Terrain on Lv 1 will NOT have LoF blocked if the target is above Lv 1, such as a on a higher level of terrain, or a or character, which may be targeted as if they are on a Lv higher than the square they occupy.

EDIT: Short Answer - no, they can't.

This is correct. He can hit another giant, a colossal, or an elevated standard or tiny figure, but not ones on the other side of the barrier on the same level as the barrier.