I'm much more familiar with playscripts than screenplays. I know that when a character onstage speaks directly to the audience in a playscript, it's as an aside, marked in parentheses, like this:

Edie: (Aside) I have a degree in Physics, you know.

But when a movie character speaks directly to the camera, is it still an aside? I've written it like this:

EDIE (ASIDE)
I have a degree in Physics...

I did it this way because in the formatting screenplays guidelines on here, it says when you're doing a voiceover, its laid out like this:

EDIE (V.O.)
This is Meze. I come here most nights...

And when you have a character speaking offscreen, it's like this:

EDIE (O.S.)
Hello, my name is Edie Muybridge, I'm with Welsh Water...

Basically, not in parentheses but as part of the character line. Is it correct to do the same for aside? Or would I set it out like this?:

EDIE
(Aside)
I have a degree...

As you would do parenthetical directions? Is it even called an aside? Or something else?

I also wanted to do an offscreen aside. At the moment, it's written like this:

EDIE (ASIDE O.S.)
It's going to be lush.

Any advice would be greatly appreciated ;D

Just realised I messed up the formatting of the false playscript excerpt.

EDIE
(Aside)
I have a degree...

is how it's supposed to look.

I can't remember seeing (ASIDE) (direction) or (aside) as parenthetical in a screenplay. I think it's more typical to explain that the character is speaking directly to the camera, whether it's a direction next to the name:

EDIE (TO CAMERA) or, (to camera)
I have a degree, you know.

Or a parenthetical, which is how Woody Alleny does it in ANNIE HALL:
ALVY
(To the camera)
Boy, if life were only like this!

And so does ALFIE (which is based on a play):

ALFIE
(to CAMERA)
I know...humble digs...not exactly
not exactly what you'd call a panty peeler....

see egs at dailyscript.com

I agree with the poster above: it's more usually put (to the camera) or (to us).

Have a look at this: http://www.bbc.co.uk/writersroom/insight/downloads/scripts/STM.pdf

When the MC is speaking to the camera, it is written as "(to us)".

As for offscreen asides, I think it would be better to write that as a voiceover, instead, unless your character is the only one in the scene/room/etc. so that it is clear that they are speaking to the audience.

Hope that helps! Good luck!