I've been working in Thailand for the past year and a half. I will leave for a month in Vietnam when my contract expires. I will return to Thailand for about 5 days and then I'll be in Nepal for 30-45 days and then back to Thailand for another month so. Should I enter on an exemption (I'm a US citizen) when I come back from Vietnam and apply for a tourist visa in Nepal?

If you don't have a history of abusing exempt entries you should not have trouble doing 2 especially if flying in. But always safer bet to get a visa.

As long as you have onward flights dated within 30 days of your entries to Thailand, to satisfy the airlines, you could enter twice on visa exempt entry. The second entry could be extended by 30 days (1,900 baht) if needed.

If you get a tourist visa from Vietnam you would have to use it on your first return to Thailand. Hardly worth it if you plan to leave after 5 days and be away 45 days. However, you could buy a re-entry permit (1,000 baht) on exit to Nepal. On your re-entry, which must be within 60 days of your tourist visa entry, the IO will stamp you in for the balance of the original 60 days. In your case that could be as few as 10 days. At the end of the 10 days you could apply for a 30 day extension of stay for 1,900 baht.

If you plan to enter with a tourist visa it would be better to get it from Nepal.