To switch all your traffic over to Google Apps, the only thing you need to do is update your MX records to point to their servers.
I assume that this is what you did? Or did you update your A record for your existing MX records to point to the google server?
If all you did was update your MX to point to the Google servers, then you should still be able to log into your old POP/IMAP server using the old settings.
However if you updated your A records for your MX target (say,
mail.example.com) to point to the Google IP address, then you've got a few options:
Create a new A record (say,
oldmail.example.com) to point to the IP address of the old mail server. Then connect to that.
Point your mail client's POP settings to the IP address of old mail server (instead of
mail.example.com, point it to