Buddhism is a philosophy, not a religion (ie. No god). Some cultures have attached religiosity and religious trappings to it, but at core it is a philosophy. Which is why it sits well with many modern, probably atheist, possibly existentialist, thinkers.
Yeah, there are quite a few concepts in buddhism i can't wrap my head around either. Karma being one.
The 'no soul' bit, as far as i have understood it, is the basic premise that everything is impermanent, implying there is no individual or permanent 'soul' and, ultimately, what we are is pure awareness. Pure mind. (not the thinking mind - not the intellect - but actual awareness itself)