We use the standard orange cleaning solution that comes with the steam cleaner
Nothing special.
I haven't done a steam cleaning in a while, it's probably a good time to do that! We try to always take our shoes off when we come in, but we don't make visitors do it, so things do get dirty.
I never thought about bare feet causing oil problems - but I love being barefoot. So I think I'll have to live with oils to clean up, vs always wearing socks, which I don't like