In my opinion:
Merge - you take one or more things and mix them together resulting in one cohesive thing. Merging lanes on a highway, 2 or more lanes become 1 and from then on you never knew the one lane came from many.
Integrate - you take one thing and make it fit into another. Integrating immigrants into a culture would mean you teach immigrants how to conduct themselves within another culture.
Incorporate - you take one thing or parts of one thing and blend it in with another. You have two plans to build a house. The first plan has a pool and shed while the 2nd plan does not. I take the plans for the pool and shed and add them, incorporate them, into the 2nd plan to build the house.