Can I put a preprint of a paper on arXiv without informing my co-authors? I am the main author and have three co-authors on a paper that I have been working on for quite some time now. Two of them have given me constructive suggestions and do think that the paper is a publishable material. 

However, the other one, who also happens to be my supervisor, has been nothing but pessimistic and rather critical in a negative way. Moreover, his suggestions are totally irrelevant to the paper. I am beginning to think that he is trying to deliberately block my paper. Believe me when I say that I am trying to give him the benefit of the doubt; I am trying as much as possible to fulfill his irrelevant and unreasonable demands.

On top of that, my contract with the university is about to end soon. I have found another position in the same field. If this paper was even submitted, which it should have been months ago, it would strengthen my CV a lot. 

Can I put it on arXiv without informing my supervisor? If not, what is the best way to deal with the situation?
First, no you should not upload the paper when not all co-authors agreed (and also not submit it to a journal).

On how to deal with the situation: If I understood correctly, there are four authors, one is your supervisor, one is you and there are two more. I think the way to go is, to get the other two authors involved in the process. For example, if you think that you supervisor has irrelevant requests for you, forward the requests to the full group of authors (including your supervisor) and ask about opinions on that matter. Be polite, focus on facts. Do not give the impression that you want to overrule your supervisor, but that you want all authors to be involved in the process. I should add that this approach may not work well with every supervisor, but I can't tell or guess what will be the case in your situation.