Provided that you're reasonably polite and that you don't act like you're entitled to have your work featured in the paper, you're unlikely to make any enemies simply by asking. Most newspapers have email or postal addresses listed somewhere; sending them an email or a letter can't hurt.
Phrases like "Are you looking for new content for [newspaper]?" or "Would you be interested in..." spring to mind. I'd also recommend picking one or two of your best pieces of writing, having them proofread by a friend - or anybody whose English you trust, really - and sending them in. Don't count on them researching you by going and reading your blog.
As far as style goes, there exist newspapers for every writing style on Earth; it depends on the paper. For a typical newspaper column, I'd say your writing style is okay, if maybe a little informal. They may disagree, though; it's hard to tell without knowing the newspaper or the editor.
Content, though, may be a problem. This may be a different story for your local newspaper, but I'd imagine the demographic that reads print newspapers and that which has a keen interest in programming don't overlap much. It's not an absolute "it'll never happen", but I think it's something you should give some consideration.