Yep, the scoring in GAA is as odd as hell, but it makes sense. I swear to god it does.

Points

In Gaelic football and hurling there are two types of score, a goal or a point.

A point is scored by playing the ball over your opponents’ end line, between their goalposts, and over the crossbar.
Heres some examples:

A goal is scored by playing the ball over your opponents’ end line, between the goalposts, and under the crossbar.

A goal is worth three points.

Goals

gaa-goalPlayers may score from either the hand or the foot in football, or the hurl and foot in hurling. A goal cannot be scored using the hand pass method, although points can be scored this way.

A goal scored by hand will count if the referee deems it not to have been by the hand pass method e.g. if a player is in possession of the ball, drops it, and punches the ball into the goal this will count.

A set of goals in Gaelic football/hurling are similar to those of rugby. The two vertical posts (goalposts) are placed 14 yards apart, with a horizontal bar (crossbar) between them, 8 feet from the ground.

If a defender plays the ball through his own goalposts, whether by foot or by hand, the appropriate score is awarded to the attacking team. A defending player may score an own goal with a hand pass.

Some cracking goals here:

and incase you are still wondering, heres a great round up of both goals and points!