Search home improvement stores for a wide gasket meant to keep drafts from blowing in around your door. Cut two pieces of gasket to fit and attach one between the counter top and the stove top and the other on the front facing between the two.
If the space between the counter and the stove is two inches or more, take advantage of it. Stick magnets to the side of the oven and attach cookie sheets, cake pans, pie plates and other metal objects. They'll be out of the way until baking time, and handy when it's time to cook.
Cut slats from old vinyl blinds to block off that open space. Snip the blinds off to the correct height to fit each space. Attach one edge of the slat to the counter with super glue. Leave the other edge unattached but slightly overlapping the edge of the oven. When it's time to move, dissolve the super glue with acetone or nail polish remover.
Purchase PVC pipe the same size as the space between the oven and the wall. Cut one piece the distance between the wall and the front of the oven. Cap this piece off and wedge it between the two objects. Do the same with the front space. This will completely enclose the space and keep unwanted objects out.