If I turn off cellular data on my iPhone, can I still use apps like SnapChat and Instagram?

I have to share a 2GB plan with two other people, and I think that if I just blocked off cellular data it would prevent me from going over (obviously).

But just personally, can I still use social applications and whatnot since the Wi-Fi will still work?

If you're connected to the Internet via Wi-Fi, everything that uses an online connection will work as long as you are connected to a wireless network. I have Wi-Fi at my house, work, and school, so I hardly use my data.

Let me help you what internet data is and what is wi-fi. In fact, both are sources of receiving internet. When you switch off phone's data it stops receiving internet connectivity. But if you connect the phone to Wi-Fi, internet is re-connected and all apps begin to work.

Apps work with internet, whether it's source is SIM based connectivity of Wi-FI.

Yes Wi-Fi will still work. Its related in the sense they are both internet connections, but not connected as in one can't work with the other.