Well, let's see:

Germany having met most of their goals of the Nazi party settle into a decline in science and physics. Most of the population is relegated to a late 19th century education system and xenophobia and nationalism reign supreme.
The US rearms the Soviets and Chinese along with the remaining Commonwealth nations. Because the US dominates (with the Commonwealth) the Middle East and the world outside the Nazi empire the Germans are also facing a severe trade deficit for many critical raw materials.
At the same time, the US using captured and stolen componets from the V-2 has already leaped far ahead of the Germans in rocket technology. The lack of a credible German spy program in Soviet Russia or the US has left the Germans in a severe intelligence deficit. The US and Russians know much of what is happening in Germany while the Germans know little or nothing of US and Soviet developments in military technology.
The US is has broken the sound barrier and is working on both several IRBM and ICBM missiles along with sub launched versions and on long range cruise missiles. The B-36 is coming on line along with the B-47 and the B-52 is close to flying. In Germany the lack of several critical metals due to import restrictions by other nations is crippling their jet engine program along with their rocket program.
The lack of highly skilled scientists and engineers with the latest knowledge due to Nazi doctrinal restrictions are falling behind the US and Soviets in technology development. Plutonium bombs are unknown to the Germans as they haven't advanced much beyond theoretical research in this area due to Nazi dislike of nuclear physics. This has kept the "best and brightest" from entering the field. Defections also hamper programs.
The US with the Commonwealth as a fleet second to none. The Germans in an attempt to finally become a sea power have tried to meet this by building some version of the Z plan themselves. Their carrier development is about a decade behind the US /Commonwealth. Their electronics are likewise considered quite inferior. The Germans also lack any credible ASW capacity against the newer US high speed submarines and GUPPY fleet boats. Of course, as they haven't had any real practice dealing with these submarines they are unaware of their weakness in this respect.
Admiral Rickover has also pushed up the construction of the first nuclear submarine and carrier as a result of the "Cold War" tensions unbeknownst to the Germans. These systems will come as a minor shock to them when they go into service.
The Germans have had little amphibious experiance during their war and have paid little attention to this sort of operation since. They have no real capacity to wage a naval war outside a traditional Mahanian style naval conflict between fleets.
The Soviets and US are also regularly making over flights of German territory much to the chigrin of the Germans. The US has also given the Soviets limited access to their SAM technology and deployed missile batteries with equivalent capacity to Nike Hercules in Russia making German counter reconnissance very costly. This increasing tension has led to calls to stop overflights.
Basically, the Germans are once again screwed. They are in a situation where they are cut off from resources they need. Many of their critical resources are highly vulnerable to attack in a war. They lack knowledge of their opponets and their opponet's economic capacity. German / Nazi politics has crippled many programs to boot.
Basically, if the Germans go to war in the mid 50's they get nuked then overrun. It isn't a pretty picture.