Otokitchi Oyajitchi Ojitchi

What is the actual meaning of the names? I know they are grandma, grandpa, and their son.

Oyaji can mean a father or old man.

Oji can mean uncle or old man.

Otokitchi's name is weird since oto means man but there's probably another meaning I don't know about.

what does the "chi" or "tchi" mean when in Tamagotchi and for example Violetchi?

It doesn't really mean anything, it's a trend in Japanese to make something sound cute by adding something at the end. There are many theories on what tch could mean, like that "tamagotchi" is a mix between "tamago" (egg) and "tomodachi" (friend) or that the "tch" (vintage tamagotchis vere usually refered as "tamagotch" rather than "tamagotchi") comes from the word "watch", since even the earliest versions had a built in clock function. I think it also sounds similarly to a suffix "cchi" which is used to very sweetly and intimately refer to someone (similar to -chan but not overly feminine or childish).

If you want to look up meanings of names, just look at the wiki. I think all characters have name meanings in there. Well, of course except these you mentioned... Don't know what's up with them, but Eternal Mametchi Fan is right. I think Otokitchi's name might have a hidden meaning in the way her name is written maybe, since in Japanese even if something sounds the same it can have a different meaning in a different alphabet.