I'm sorry, but Molly is incorrect or at least incomplete. Invidious means "tending to cause envy, anger, resentment or, simply, a bad feeling in other people". So, in other words, something you do or something someone else does causes other people to feel angry, envious or some other negative emotion. "Personally I have been put in an invidious position." This *could* mean you are in a difficult/hard situation. But the reason it is hard is because what you have to do will cause OTHERS to had bad feelings toward you.

Invidious is like 'awkward' or 'difficult'. 'Personally, I have been put in an awkward position.' or 'Personally, I have been put in a difficult position.' An easier word to remember is 'hard.' 'Personally, I have been put in a hard position.' But I believe 'awkward' or 'difficult' sound better than 'hard.' I hope this helps. :D

I would add to the answers that it is a "literary" kind of word. The reason why it is easy to be mistaken about the precise meaning--Mojave is correct, but I had to look it up to be sure myself--is that it is a word I've often read, particularly in older books, but rarely use. It's not part of my active vocabulary. I know it best as part of a specific expression, "comparisons are invidious," meaning "don't compare people to each other, it just creates bad feeling."