When I first starting vaping I had a few days of feeling a little 'off'. Nothing I could quite put my finger on but a general feeling of discombobulation that came and went. It went away for good after a few days so I chalked it up to the combination of cigarette withdrawal and starting vaping.
One thing that did help me was drinking much more water than I thought I needed. Drinking little sips of iced-water often, seemed to help clear my head.
I've never really associated vaping with sleepiness. I know that vaping helps keep me alert and I know a lot of others cannot sleep if they vape a lot before bedtime. So much so, i've seen many vapers report using a lower nicotine liquid after dinner so as to not suffer from mild insomnia.
You mentioned it occurs more with menthol liquids - are they all from the same vendor, or do they all have similar ratios of PG/VG? If so, you might want to try to mix it up a little, changing one thing at a time and seeing if the effect either increase or decrease to find out what might be causing it.