Learn English – What does “the jury is out on that one” mean

The phrase I'm out of energy means: I'm tired, and not energetic.

The phrase is used in various contexts, and could be used to describe mental energy or physical energy.

For example, a basketball player might be out of energy, and ask for a sub to come into the game, so he can rest on the bench.

Or, on Friday afternoon after a hard week at work, a teacher may be out of energy. This means – those essays her students just handed in? She will carry them home, and grade them on Saturday after a good night's rest. She doesn't have enough mental alertness to deal with them right now.

I'd also say that the phrase is somewhat figurative. Many times, people who say they are "out of energy," actually have could be more energetic, but they are just wanting to relax. For example, the basketball player is probably not on the verge of collapsing, but he probably won't play very good defense. The teacher probably could grade the papers if she really needed to, but it's not an ideal time to do so.

The expression could also be used to describe teams, too, and not just individuals:

After the German team scored their first two goals, the Brazilian team seemed to lose their energy.

This doesn't necessarily mean that the Brazilian team looked tired, but it could also mean that they looked discouraged, and played with no heart.

"I can't talk my way out of." Is it an idiom?

Yes, to "talk one's way out of" is an idiom. It means to evade negative consequences by convincing the imposer of those consequences not to do so.

Examples:

I got stopped for speeding on the way home, but talked my way out of a ticket.

I was sure he was going to get fired for that, but he talked his way out of it.

It's is worth noting that a way out is itself an idiom, meaning an avenue of escape. In a literal sense, "a way out" is any exit from a place, from a door in a room to the path out of a maze to the route out of a cave system. It is used metaphorically for any means of escaping a bad situation or dreaded consequence, comparing them implicitly to a trap or prison. So people speak of needing to find "a way out" of relationships, jobs, responsibilities, contracts, etc.

Thus to "talk one's way out" of something is to escape a situation by means of one's verbal interpersonal skills.