Actually, it is hard to compare those particles. They have several use cases and, as John Smithers already pointed out, can be translated with other words as well.
Anyway. What these have in common is that they can be used to place special emphasis on what you've just said. You can often replace those words with the particle ausgerechnet. In the following two sentences you actually can place all four particles but interestingly the position in these sentence matters.
Warum passiert das gerade [or ausgerechnet] mir?
Warum bloß [or nur] muss ich immer dran glauben?
You hardly can define or explain when which of those words is commonly used. It's a feeling of languages to determine the correct word. Though, it would sound only slightly odd if you'd interchange them. But be careful. The meaning can change as in
Warum passiert das nur mir?
what is different to the sentences before since the emphasis is on the fact that you are the only one.
These words, however, are not always interchangeably. The following sentence in which you emphatically say that you want to be left alone only bloß and nur are common. The slightly different connotation of those particles is explained in John Smithers answers. But note that gerade would sound very weird either way.
Lass mich bloß in Ruhe.
Well... Actually in combination with mal you can place gerade and eben in that sentence as well but again you create another meaning.
Lass mich gerade mal [or mal eben] in Ruhe.
This sentence expresses that you are very busy or need to focus on what you're doing and you ask for leaving you alone for a minute.
However, to fully discuss the differences and overlaps in meaning you could write an essay; hence, the only way is to gain the feeling when to use which one.
Regarding your question which particles are representing the English just you need to remember that just does have a lot of meanings. Here are some more possible German particles but this list is incomplete for sure.
What did you just say? - Was hast du auch gleich gesagt?
I was just going to phone you. - Ich wollte dich eben anrufen.
That's just impossible - Das ist einfach unmöglich.
How does it just happen? - Wie ist das eigentlich [or überhaupt, or denn] passiert?