I agree with Adam's answer in general, but would just add that context is quite important. You 'combine' ingredients when following a bread recipe, when two lines of traffic arrive at an intersection they 'merge', and a lamp might be made by 'fusing' a metal part to a glass part. So maybe you can see the result is a bit different... once they have been combined you can't separate the bread ingredients into their separate parts...the two lines of traffic become one but are always composed of individual units (vehicles) and the "join" happens in many different places and exact way they join isn't defined by the word 'merge'.. but fused materials are joined but always separate because you can identify what part of the lamp is metal and which is glass... But as I said before... it depends on the context

They are synonyms for the most part and mean the same thing. They can all three be used as transitive or intransitive verbs (that is to say, taking an object or not taking an object).