Can I submit published articles to arXiv as well? I have several math research articles on my site.

Some of my articles are published in open access journals.

Some of my articles are currently available only from my site.

I may probably publish something in a closed access journal.

The question: Should I put these kinds of articles at arXiv (and possibly replace articles on my site with redirect to arXiv)? I think yes, because it would increase visibility of my articles, as many people search on arXiv and/or receive arXiv mailing lists.

Is it ethical to put an already published article also at arXiv?
I suggest you first of all check 


the copyright transfers you signed
the publisher's FAQ on rights you retain as author
Many publishers nowadays allow you to self-archive the version of the manuscript that passed the review. Some do not allow self-archiving on public repositories (but e.g. Elsevier makes an exception explicitly for arXiv). For a quick overview have a look at the SHERPA/RoMEO site.
and your local copyright legislation.
E.g. the German UrhG now allows secondary publication (e.g. to arXiv) of your manuscript (including the version with exactly the content of the published paper) for journal contributions that were financed mainly by public grants.