There's a lot of subtlety involved and it's hard to precisely define the differences. In general, I would say that all three are interchangeable and have the same meaning. 'Only' is probably the most common word, and is applicable to almost all situations. 'Just' is marginally more formal, and has a couple of extra meanings. First, 'just' can mean the same thing as 'fair', usually in the context of a decision or judgement. "Sending him to jail was a just decision". Secondly, it can be used for a recent thing in terms of time. We can say: "I have just arrived" to mean "I arrived (for example) one minute ago" The sentence: "I have only arrived" instead means "Arriving is the only thing I have done" and would probably sound weird. We might also say "I have only just arrived" which means the same as "I have just arrived", but with perhaps more urgency. Finally, "merely" is more poetic or formal. It is usually used when discussing measurements, rather than numbers/quantities. "It is merely me" is technically valid, but sounds very weird. On the other hand "It is just me", or "It is only me" are both very common. However, "He weighs merely 50kg" would not be incredibly uncommon. We also use the terms quite often in idiom. For example: "I am but a mere human" or "I am only human" are ways someone might say "I'm not perfect".