They're very vague, yes. I work from when Simon says that River can't not feel, that she's aware of everything all the time; then I add in her ability to shoot without looking at the targets, and what we know from the BDM about her mindreading and other psychic abilities. Early on, she might not be able to fully distinguish memory from reality, nor thought from speech.
I assume her psychic powers are a combination of mind reading and analysing probabilities; but early on in the show, she's overwhelmed by the input and so her analyses come out, as you rightly and poetically put it 'tangled in metaphor'