Here is what I think will happen...
Goering takes power, and eliminates the SS. Goering essentially is the only Nazi that can effectively control the military, so he naturally would be the successor (With Hess as a glorified secretary of course). The racial laws would probably be minuscule, or non-existent. I think Goering would be a lot slower with bringing Germany up from the damage of World War I and the Depression, and will probably go as normal as OTL (Except without Hitler).
Austria and the Sudetenland will probably be forced into Germany at some point, but with less opposition due to Goering probably being more respected than Hitler. Now, Goering probably would not be an enemy during World War II, and can probably rally Western Europe against the Soviets, leading to a whole different World War II I think.