As with most words, they are similar and in some cases interchangeable, but have subtle differences as well.
--Sustain refers to something that on it's one could not really be permanent in the long term (i.e. it is unsustainable). You could say "the government created a national park to sustain the region's natural resources." This implies that without the government's help, people would cut down the trees, hunt the animals, etc. Sustain can also mean to bear the burden of something, again that would fail on it's own, i.e. "I had to sustain his weight when he broke his ankle and could not walk."
--Uphold is more for something that is being brought to question within a society, e.g "the court decided to uphold the law," meaning some people were arguing against the law, but the court kept it in place. you could also use sustain here.
--Support to me means to agree with or offer your help to someone, e.g. "I will support your dream of becoming an actress."
--Back up can have several uses, but it usually means to ensure that something is correct, justified, successful, etc. e.g "I backed up my argument with evidence" or "I backed him up during the debate," implying that this person helped argue for his friend by providing new points or evidence.