Stupid iPhone still gets texts?

I changed from an iPhone 4 to a basic phone but my iPhone is still receiving messages as well as my new phone. And it still has Internet without Wi-Fi

Your iphone is only receiving iMessage texts because you are in Wi-Fi. Turn your iphone off or you can go in the settings of your iphone and turn off iMessage. The same thing happened to mine when I water damaged my iphone.

Delete your account from your itunes or deactivate it.
Change your wi-fi connection.