I personally think a good anchoring point can still be weird. I mean, take this example: The book is about demigods playing an ultra-violent version of soccer. Now, a lot of the readers who would pick up a book with that blurb are the sort of people who have a good understanding of the nature of demigods. The point is, even though it's weird to have the demigods be the point of contact in the story (the closest thing to a human element) plenty of people will happily read a book about them because these are the sorts of people who CAN put themselves in the shoes of demigods.
Now, your story may be even weirder (probably is - demigods is a pretty standard fantasy trope) but there'll still be people out there who can connect - you don't need a normality in there for the sake of the readers, because most readers are intelligent enough to be able to go with the flow. In fact, I'm one of those readers who likes having to connect with the weirder side of things. I love first person stories about vampires, for instance. Now, I'm not a vampire, and logic would say that you need to make the MC a human for my sake, but I'm fully capable of putting myself in the vamp's shoes, especially if it's written well. So for me, the book just gets better and better by having a non-human MC - which is a weirdness, but one that just works for me.
So my rambling point is, you don't have to have normality in there just for the sake of it. People can connect to all sorts of things. If it's something you, as the writer, have been able to connect to, then surely plenty of readers will connect as well.
Good luck.
Oh, and the parts that don't feel right need the little red pen of justice.