When a conversation is petering out or one person just wants to move on or discuss something else they use anyway.
"...and then he said he liked it"
"So anyway, what are you up to today?"
Like the example you use "What are you doing anyway?" would come in conversation. The anyway word is not needed, it just makes the transition away from what you were talking about less abrupt. If you just walked up to your friend you would just say "What are you doing?" or maybe "Hi" first :)
It can also be used rudely sometimes as a one word reply. Perhaps when someone is telling you what do or scolding you.
In any way or manner whatever: Get the job done anyway you can.
In any case; at least: I don't know if it was lost or stolen; anyway, it's gone.
Nevertheless; regardless: It was raining but they played the game anyway.