Learn English – Should “bring a plate” be taken literally

Let someone in or let someone out means to enable someone to come in or get out of somewhere.

Hi, the door is locked. Could you let me in, please?
Hey! I want to go home! Let me out of here!

If you would address me with these lines, I could let you in to my house, or I could let you out of the cage.

As a result, you would probably get into my house, or get out of the cage.

Now, if the person that you let in or out is yourself, then you do not need anyone else to allow you or enable you to get into or out of something. So if you have the key to my house and to the cage, you can say:

Hi, the door was locked. I let myself in.
I wanted to go home, so I let myself out of there.

I generally consider "idiomatic" and "idiom" to have approximately the same relationship that Damkerng T's comment suggests: an idiomatic construction is any construction that a native speaker would prefer for a given use, while an idiom is a set and rather quirky phrase or pattern that's unusual enough to identified and talked about by laymen, not just linguists. Conveniently, that's also the dictionary definition.

Basically, yes, the question phrase is idiomatic; it's not really (much of) an idiom, since it's not very odd or exceptional or memorable.