Is it good for kitchen cabinets?

Unless the cabinets are extremely grimey, I don't know why not, as long as they're wood.

Can this be used on oak hardwoods? I was told to only clean with diluted white vinegar.

Absolutely! I used to use a homemade concoction which included diluted white vinegar until I found & fell in love with this Method Wood Cleaner. You will love it. Seriously!

Is this safe to put on wood furniture where cats walk?

I haven't had any problems with my cats and using method. It's one of the healthier cleaners.

Ok does it actually clean the wood? We know it smells ok. We know it has a bit of polish shine. Can anyone state it cleans prints and cabinet gunk off

Yes it does. It actually makes it shine vs other cleaners I've used. I'm not sure what gunk you mean, if you mean the typical fingerprints and sticky spots, yes it will get that off! Overall I recommend method cleaner over almost anything. It smells incredible and it works well!