Pardon me and excuse me are almost the same.
In normal everyday culture, you would use them if you were interrupting someone and want their attention , or to ask to get past someone in a crowd. Excuse me is used more often than pardon me.
Forgive me - That would usually be reserved for asking forgiveness if you were to do something wrong to someone. you would ask for forgiveness. Like if you lied to someone and they found out, or you forgot a family members birthday. Usually reserved for some big mistake.
Sorry - can be used in many ways!!
For simple things, like if there was a little confusion when you try to walk past a stranger, you would just say 'sorry' in passing.
Or if you accidentally knock something over that belongs to someone else
Or if during a conversation with a friend, you say something to offend someone ' sorry, I didn't mean it that way'
Or even being honest, you can use it to mean that you do not mean to offend someone "I am sorry to say, but you smell bad" :)