I'm going to try my best an avoid a long story...
I messaged this girl on Ok Cupid last year, we exchanged numbers and within about an hour of texting she calls me and invites me out to a house party. That night, we end up going back to my place and hooking up. After that night we pretty much went our separate ways.

So last week, after many months, I send her a message and she sounds excited to hear from me. She says "Hey you! I lost your number a while back. What is it?"

We hit it off right from the bat. After a long conversation I invited her over for wine and hot tub. She comes over and talks about how recently she has really hated men and jokingly said she was considering becoming a lesbian. She mentioned how she had thought about me and was happy we had began talking again. We end up having sex and it turns out I was the first person to have sex with her in 5 months since her last disaster relationship.

She met my parents that night, and the following morning we got lunch and she introduced me to her parents. She sent me a text saying "It was night to meet your parent, they were really sweet and I cant wait to see them again =)"

Since then we've talked on the phone and she has said, "we should hang out this weekend or sometime soon, it would be nice to see you again."

I invite her out via text and she doesnt even bother responding for 2 days. I get a text saying "Sorry hun, Ive been super swamped with work :/"

Im getting mixed signals. She likes me but blows me off. Is she testing me? Should I act like its no big deal? I like this girl and dont want to mess it up.

Hey man, no matter how busy with work, she SHOULD MAKE time to answer to your texts... she is either disrespecting you big time, or shit testing to see how you react. You should keep things casual and see where it evolves from now on... thinking in the frame "don't want to mess it up" will cause you to mess it up, as you will put up with more and more shit from her...

how's this for a strategy: when she doesn't respond the same day to your text inviting her over, tell her "made other plans" and get her to understand indirectly that if she doesn't respond, you will not wait for her forever... don't give more than you receive, otherwise she will take you for granted... the "I can have that guy anytime I want" mindset will not make you attractive in the long run...