The difference in usage is that although, though and even though are all conjunctions, whilst in spite of and despite are both prepositions. So usage requires:
although + clause (subject + verb + …)
though + clause (subject + verb + …)
even though + clause (subject + verb + …)
in spite of + noun (or Noun Phrase)
despite + noun (or NP)
∙ 'Our new neighbours are quite nice, though their dog is a bit of a nuisance.'
∙ 'She insisted on keeping her coat on, although it was extremely warm in the house as the central heating was on.'
Though is often used with even in order to give emphasis:
'I managed to get good results in my exams, even though I went out four times a week when I was supposed to be revising.'
Whilst despite might be thought more formal than in spite of - it is, after all, one word rather than three - there is really very little difference in usage between the two:
∙ 'Despite the appalling weather, they succeeded in walking to the top of Ben Nevis.'
∙ 'They decided to get married in spite of the huge differences in their ages.'
(examples taken from www.bbc.co.uk)
although/ even though/ though vs. despite/ in spite of:
For an explanation on the use of these expressions press here.
For more examples and exercises press here.