It's more or less synonyms, in the usual case (I am sorry for what I have done). - Être désolé = meaning that you regret doing something (Je suis désolé de t'avoir fait du mal = I am sorry to hurt you) or that something happened (Je suis désolé que tu aies perdu ton père = I am sorry that you lost your father) - Je te demande pardon = You ask for forgiveness (so for something **you** have done "wrong") - Excusez-moi = Excuse me, forgive me. So you can see that the last 2 ones are focused on what you have done (I ask for your forgiveness) or what you want (please excuse-me); the first one could be used not only about you. Hope this helps.

Long story short, Desole is "sorry" , pardon is pardon excuse moi is excuse me, and pardon is pardod LOL... But joking aside, if u learn them by their equivalent it's easy and helpful.