Transferring Files
Files can be transfered to and from Nokia 3650 using bluetooth OBEX protocol. Most Linux distro (well at least Fedora Core 3) already has OBEX tools installed and ready to be used (just check your GNOME/KDE menu). Symbian supports OBEX transfer, so this is not limited to 3650 (I have tested Nokia 6600 and it works too.)
Infrared
I have only tested the infrared connection for sending SMS using AT Command, and not for anything else, not even using it as a modem
Bluetooth
The Nokia 3650 bluetooth can be used to transfer files, as a connection for modem (GPRS modem), and to send SMS from the computer. Reading SMS is not possible though. The Gnokii project is still working on a full support for this Phone.
Modem
I have used 3650 as modem successfully using bluetooth with a custom pppd script.
NFS Server
An NFS Server (yes, a server) exists for Symbian Series 60 phone (and others), it allows you to mount your Symbian files to a Linux system. Since Symbian is using mandatory file locking, not all files can be copied to Linux (file in use, and not shared). It is a very fast way to copy files from and to a Nokia 3650 (well, a card reader is faster for copying large files, but you need to turn off the phone to take out the card reader).