How to close gap between cabinets and drywall?

Insulate: you can't insulate the cavity behind the drywall unless you blow in insulation. Actually Home Depot rents a machine for blown in insulation. It is like a reverse vacuum, it blows instead of sucks. You will need to make a few 1 1/2 inch round holes in a few places to stick the hose into. Gap: Go the the molding and trim aisle of lumber yard and find some "scribe molding". It will be flat and thin, Doesn't appear there is anything to nail to based on your pic so get a tube of Liquid Nails. Place a scrape piece of scribe mold up and lightly draw a pencil line, then put a thin amt of Liquid Nails. You can also use contact cement. If the don't make scribe molding wide enough to cover your gap go to the aisle with pine wood lattice

Before you purchase wood lay out on a piece of paper the areas to be covered and measure. Lumber is sold in distinct lengths, usually 8, 10 ft. Lay out amt of materials needed. For example if you need a 5 ft piece that means a 3 ft piece will be left over. See where that fits. If too short plant to purchase enough so each is one piece, don't try to piece small pieces into a long space. Oh, and prime and paint it before you put it up but after you cut it to size.