I’m assuming that the easy bake oven look is best described as un-even top and swirls in the icing, with emphasis on the un-even icing texture.
It may or may not go without saying, but just in case: “top” the cakes before you fill and assemble.
If you are not using and off set spatula get one, it is virtually impossible to ice a cake smooth with out one. Also a turntable might help. Crumb coats aren’t just to keep unsightly crumbs out of sight. If you put the crumb coated cake into the fridge and let it get nice and cold, the butter in the icing will get “hard” and kind of form a “shell” around the cake. This “shell” allows you to put more pressure on the cake when applying the final coat of icing. Much like spackling dry wall, the more pressure you use, the smoother the application.
The biggest trick is to make continuous strokes. The more you pick the spatula up off the cake surface the more lines and swirls you will have.
Start with the sides and do the top last. Once the final coat is on and mostly smooth if you still have a problem “hot knife” it. Heat the off set spatula with hot water, dry it off and lightly go over the surface. The heat will cause the butter to soften and the spatula will glide right over, smoothing out the rough spots.