J'onn J'onzz restored Team Flash and Team Arrow's pre-Crisis memories. J'onn using his powers to give their memories back causes their post-Crisis memories (which they had of the new post-Crisis timeline until he restored their other memories) to be overwritten. So, that's why Team Flash remembers the other versions of Wells they've met.
When the multiverse was reborn, all versions of Wells were mashed together into the mind of Nash Wells. So, because of this, he now experiences visions of various other iterations of Harrison Wells, like Harry and Sherloque, who are usually trying to tell him something, communicating with him (for instance, leading up to "The Exorcism of Nash Wells", Nash sees Harry and Sherloque, and when the latter appears, Sherloque's eyes glow red. He's trying to warn Nash that, in addition to the other Wellses, Eobard Thawne's mind is also tangled with Nash's.) That's because Eobard had Earth-1 Wells's DNA, since he used future tech to assume Wells appearance and impersonate him to build the particle accelerator to turn Barry into the Flash to harness Barry's speed to return to the future.
However, in "The Exorcism of Nash Wells" Eobard is expelled from Nash's mind; leaving Thawne in a non-corpreal form, now existing as negative tachyons. In the same episode, Team Flash concludes that there's no way to separate the different brainwaves of the various Wellses from Nash's mind. As a result, the visions he experiences of other versions of Wells will continue, but Nash expects he'll get used to it.