Q:

Must the Orc's Agressive movement be in a straight line directly toward the enemy?

The Orc's Agressive trait (Volo's Guide to Monsters) lets you use a bonus action to move toward an enemy, as long as you finish closer to him than you started.
Must this movement be in a straight line directly pointed at the enemy (ex: doesn't work if there is an obstacle in the way you could otherwise pass by moving at its side) ?

A:

You do not have to move in a straight line.

Aggressive. As a bonus action, you can move up to your speed toward an enemy of your choice that you can see or hear. You must end this move closer to the enemy than you started.

Nothing about this feature indicates that you must move in a straight line.  The only condition is that you must end up closer to the enemy than you started.  You could actually move away for part of the movement or end up behind the enemy, as long as you are at least 1 square closer (if on a grid) than compared to where you started.
Some DMs might rule that you must move toward the enemy for every square of movement, but even this would not require a straight line (you could use diagonals).  I interpret the meaning of moving toward the enemy as a constraint on the entire movement and not on every piece of the movement.  The wording is a little ambiguous though, so there is room for differing opinion.

A:

The exact wording is (VGtM p. 120):

Aggressive. As a bonus action, you can move up to your speed toward an enemy of your choice that you can see or hear. You must end this move closer to the enemy than you started.

There is nothing there that says you have to go in a straight line, only that you must move “toward” and “end this move closer”. So long as you don’t move further away during the move (i.e. each step brings you “towards” or, at least, not away) and end up closer, you have met the conditions.

