These (apart from perhaps deep down) often overlap but have their own uses. Best to use a dictionary first but I can explain their usage in a basic overview. Actually is used the most. It can be used in a variety of ways and in variety of positions in a sentence. You can use it a bit like "really". In fact is used slightly less commonly than actually and has a slightly more formal feeling to it and is often reserved for realisations and more 'factual' statements. Indeed is quite formal these days and is used more as an affirmation e.g "absolutely, I agree". Deep down has more of an emotional feel to it e.g. "Deep down I knew something was wrong". It is quite different from the others. Hope this helps a bit.