"Excuse myself" would not generally be used on its own. However it may be used to describe a time that you removed yourself from a social situation (a dinner, or a party, for example):
My telephone rang, so I excused myself from the dinner.
If my wife calls while I am at the party, I will excuse myself, step outside, and answer her call.
While the present tense of this would simply be
Excuse me, I must take this call.
In the above statement, you are asking the people around you to forgive you for leaving. You are, in essence, apologizing. It's a way of expressing that you enjoy their company. "I am sorry, please forgive me, but I must go."
"excuse myself" is still expressing that you enjoyed the company around you, but you didn't find it necessary to apologize for leaving. Instead of bothering the people around you, for example if they are busy and you don't want to interrupt, you excuse yourself and leave without saying anything.
For 'excuse yourself', this would generally be used to describe the second person example of the same situations.
If you must talk on your phone, please excuse yourself and step into the hallway.
In some cases it can be used on its own, as a command to someone, for example if someone does something socially impolite, you might say "excuse you!" or "excuse yourself!" For instance if I say something rude, or I burp.
"excusing", as a general verb, describes a very polite or socially acceptable way to remove yourself from a situation.
On the other hand, the noun "excuse", would be a reason for leaving, or having performed some action that requires an explanation.
I called in sick to work yesterday. My excuse was that I had to see the doctor.
There is no excuse for missing your son's baseball game.