IIRC American forces invaded Chinese mainland in the last stages of the war. Due to power armor and "enhanced troops" (sounds like FEV to me) they were advancing rapidly. That is when the Chinese escalated to full nuclear. Based on this, there would likely be survivors/descendants of the American forces in Manchuria. Likely they'd have a set-up similar to Vault City with locals used as labor for the American master race. Pre-war US seemed pretty nazi to me after all. Compared to Vault City, the survivors might have ghouls and super mutants among them, though.
China itself would be really badly hit. Remember, USA is fucking huge geographically. China is physically smaller but packed with people. Nuclear strikes had been concentrated relatively tighter compared to US, where there'd sometimes be hundreds of miles between targets. So I think things would be physically worse than in the US. Culturally, China has always been a patchwork of petty kingdoms that are in "good times" forged together and in times of trouble split into squabbling mini-states. There isn't even one Chinese language, but several. It is realistic to expect that this split had happened again among the old borders. Added to those old cultural units would be the urban sprawls on the coasts. They'd be likely absolutely ruined by the war and filled with raiders, ghouls and undesirables. Plus the occasional free state completely different from Chinese traditions.
What comes to their neighbours... Since the Americans invaded China, it stands to reason they used Japan as a staging ground. So there would be remnants of American troops and military infrastructure there. This would mean loads of supplies destined for the invading armies. Some of the resources and the people might have survived. Japan, on the other hand, would be fucked. It is a small and urban country, easy to obliterate with nuclear weapons. I suppose nukes big enough might have caused tsunamis or triggered earthquakes. I think it would look something like Capitol Wasteland. The people who had survived with least casualties would be in the northern and southern ends.
Korea... I have no idea. Another devastated battleground between Americans and Chinese? Since Americans invaded Manchuria, Korea would be another logical point of entry. I think India would be fucked for the same reason as China; loads of people in a relatively small area. Like China, India has always had strong regional loyalties and identities. It would likely be split among these historical divides, with some ruined high-tech cities standing apart form the traditions. There would be horrible draughts everywhere and wars over water. India is even in contemporary times dependant on melting waters from Himalayas. Thanks to global warming, these sources of water are running out. Considering the enviromental changes in Fallouts, the situation would be drastically worse.
What comes to the global situation in general, I think Iceland and New Zealand would be most untouched by the war. Who would want to target them with nukes and they are far away from other targets. Australia might have been hit by China and would be enviromentally fucked anyway like India. Do we know anything about South America?