I'll summarize the ones you are asking.
Infinite Stratos is not mecha anime, whoever categorize it doesn't really know their stuff. Mecha means robot, and IS doesn't have those. Don't know if you've seem Mai-Hime franchise, it kind of like that. Basically the character wears power up suit. Think of it as Sci-Fi verson of people wearing full fledged knight armors. Also the anime actually have very little fighting, so I don't see it would be a problem for you.
Asobi ni Iku yo is different. There are robot there, but they are used as service robots. basically the story is like DearS where alien come to earth for study purposes. While you might not like cat girls, the anime is actually pretty good on justifying them. The premise of the series is that those cat girls are aliens. However, I still suggest you give it a shot, at least with 1st episode as the cat girls in that series
doesn't behave as your stereotypical anime cat girls but more like human cosplaying as cat girls and the series actually make fun of that quite often. And it really is a pretty enjoyable series that I think you would like it.
Who knows, you might change your mind on hybrid people like you did with harem anime.
Dog Days is similar, but instead of Sci-Fi setting, the premises is that the main character got summoned to a magical world (ala zero no Tsukaima)where poeple over in that world has dog (cat) ears and tail. Again they rarely act the way to stereotypical animal people and the tail/ear focus are minimal. Again I would suggest you at least give 1st episode a shot and see how you feel.
To Aru series actually have three seasons. The main series
To Aru Majutsu no Index has 2 seasons with the main character being a kick-ass guy that tend to attract female despite his tendency for "bad luck". (there is a reason for that though) The third one (actually chronologically the second ) is called
Toaru Kagaku no Railgun, that series is a spin-off centers around the #2 lead female (some might argue #1) from the Index series, Misaka Mikoto. Because of her immense popularity, a Spin-off Manga was created in addition to the original light novel. It basically expand the story on Index Season 1, as well as provide a few original story that ties to her side of story which would later intertwined with the main story as well. In addition, the Railgun anime helps to fill in some background/setting details that Season 1 skipped due to episode constraint. With that being said, Railgun is funnier and more light-hearted than Index and if you end up liking Index series, you shouldn't have problem enjoying Railgun series.