Can I start with Dark souls 2?

The story isn't really connected with Dark Souls 1 other than it's the 'same universe'. At least, not that I noticed.

Both games have huge amounts of lore you can dig up by finding things, and reading online where you can't be bothered to find things ;) - However if you've played DS1 you'll have a good idea of the combat and other ideas in DS2. But this doesn't mean you can't just jump in with DS2, it'll just take you a bit longer to pick up the games style.

(I've not played Demon Souls so can't comment about that).

There really is no necessity to play 1 before 2, the story is not linked in any way other than a "repeating cycle".

That being said however, there are references in Dark Souls 2 that link back to Dark Souls 1. Eg, you can find the orginal Lords of the Flame in DkS 1, and only references to them in 2.

The storyline and Lore can be a bit vague if you're not really looking, but IMO, I would suggest playing them in order, just to get a proper understanding of the universe. (Also, I would suggest playing 1 first, otherwise you'll likely get annoyed by the clunky controls compared to 2).

In regards to Demon's Souls, there is no relation whatsoever to Dark Souls.