1) "Kinda" is the same as "kind of". It's the lazy way of writing the phrase, and should be reserved for informal texts or e-mails between friends. It's slang, so it's good to recognize it, but it wouldn't be something you'd write in a professional or academic setting.
Ex: "Are you excited about the new job?" "Kinda, but I’ll be more excited when I finish the projects at my current job."
2) Using "a kind of" means you're labeling something or putting it into a category. An orange is a kind of fruit. It belongs to that category.
"Kind of" is different. It means something is almost a certain way. So using your example: “I’m kind of annoyed when she comes to the house.” Maybe I have a friend who I enjoy seeing, but who leaves a mess in the kitchen every time she comes over. Since I like to hang out with her, I’m glad when she comes over—but, in spite of the great conversation, I’m a little annoyed, too, because she leaves such a mess! I’m not completely annoyed – just “kind of” annoyed.
“Kind of” can also mean there’s a little bit of similarity to something else.
Ex: “When I do yoga, I look kind of like a walrus under duress”.
3) "Sort of" has the same meaning as "kind of".
4) When using "sort of" and "kind of", you can use it as a one-word response: (“Do you like caviar?” “Sort of.”) Or a response that you expand on: (“Sort of. Until I remember I’m eating fish eggs. Yuck!”)
You can also use it before a verb: (“I kind of enjoy boating, as long as the waves don’t get too high!”)
Or after a verb: (“I look kind of like a pigeon in these shoes.”)