"each other" and "one another" are alternate ways of saying the same thing. 'each other' is more common when only two people are involved; 'one another' is more common when more people are involved. However, either can be used in either case without any loss of meaning. These must be used only in the plural. The action goes from one person to another, different person; and the reverse.

They love each other. They love one another.
They write to each other. They write to one another.

Impossible: She writes to each other. He loves one another.

'themselves' is different. This can be used in the singular (changing to 'himself' or 'herself', of course) or in the plural. The action goes from any one person to the same person, not to a different person.

They thought very highly of themselves. (Each person thought highly of himself. No information about whether any of them thought highly of some person other than himself.)
She cut herself with a butcher knife. (She did the cutting. She received the cut.)

Contrast with
They cut each other with a butcher knife. (Each cut someone else. A cut B, and B cut A)