Ore means I or ME in Japanese. It's just another way of saying I in Japanese, just like Watashi, for example. (there are lots of ways)
And the little hiragana -tsu thing you are talking about isn't pronounced.
In hiragana, you have 2 kinds of these tsu symbols, the big tsu(which is pronounced as tsu) and the small one you are talking about.
This small one indicates a quick stop in a word, a swallowing stop(you don't have to really swallow, though), more a terse silence.