These are all Sentence Connectors which create links between sentences. There are many types of Sentence Connectors, but here we only have two types.
The first are Contrast Connectors, which express a difference or contrast between two sentences regarding the information that the two sentences share. These are all Contrast Connectors: "aside from", "apart from", "except for", "except", and "besides"
These can all be used to say the same thing. The most commonly used ones are "besides" and "except (for)". For example:
Aside from/apart from/except (for)/besides my brother, everyone in my family likes to eat spinach.
Meaning: In my family there is my mother, my father, my brother and me/I. My mother, my father and me/I like to eat spinach. My brother doesn't like to eat spinach. Everyone in my family likes to eat spinach, except for my brother.
I'm so tired. I don't want to go anywhere besides/except (for)/aside from/apart from home.
Meaning: My friends want to go see a movie after class. I'm so tired from studying all day. I just want to go home and sleep. I don't want to go anywhere except home.
Another example: I am going out to eat with friends. I don't like Indian food, so I tell my friends, "I'll go eat anywhere except for the Indian restaurant.'
The second is Adding Connectors, which adds new information to what was said in the previous sentence. There is only one example here, "in addition (to)".
You need too buy the red dress, in addition to the black shoes.
"In addition (to)" tends to be a formal way of saying "as well as" and "also". A very informal way is "on top of that".
You need too buy the red dress, as well as/also/on top of that the black shoes
Meaning: I need to buy the red dress. I also need to buy the black shoes.