First a disclaimer - always be legal!
You may need to check what the law says about recording calls. It sounds like you should be okay with what you are planning, but even if recording your own calls you may have a legal obligation to warn others when you are recording the calls.
Whether it's possible to tap into a voip call would depend upon whether it uses encryption. You can monitor network traffic using tcpdump or wireshark, but that would then need to be converted into an audio signal. If it's encrypted then that is practically impossible to decode (unless you have the resources of a government agency).
But if you are using a computer for the voip application then you could record the audio output that is going to the headset instead.
Tapping a regular POTS line can be done with a telephone recorder / line adapter. You can search for one of those, but you may need to check for appropriate protection against electrical spikes. These normally provide the audio on a 3.5mm jack plug which needs an adapter so that it can work with the Raspberry Pi (eg. a USB sound adapter).
An alternative is just to put a small microphone near the phone and connect that through a USB sound adapter into a Raspberry Pi (although that may result in too much background noise for what you need this for).
Once you have the audio then you just need something to record it. You can do that manually through an application such as Audacity, or look at automating it using PyAudio http://people.csail.mit.edu/hubert/pyaudio/