I installed a Greasecar kit on my neighbor's TDI and tapped into the heater hoses as per the kit's instructions. Since then I've been told that it's better to go in series with the oil cooler hose. Is it worth replumbing the system to do this? And does anybody know the hose size?

Nobody knows? 5/8"?

What model car is it? I tapped my 96 Passat off the line from the engine head that goes to the heater core. I used 3/4" hose, but where it connects to the head is larger so I spliced into that hose. Run it in a series for the best heat gain. Even if it is supposed to be 5/8" hose, 3/4" can be clamped down to fit.

It's a '99.5 Jetta. The system is currently in parallel with the heater core. I have been told to make it in series with the oil cooler hose instead.

I haven't worked on a 99.5 Jetta, so I am afraid I can't be of much help.

Parallel with the heater core is good.

What is difference between series and parrell?

I recommend the heater core over the oil cooler. I have a similar '98 TDI.
iirc we had a thread on the o.c. as heat source here and it's possible for the water temp. to get above 190*F.

I did tie in my TDIHeater at the oil cooler and wrote about it here:
http://ctbiodzl.freeshell.org/votdi.html#Conversion
Search to
"Zerostart tank heater installation."

You can find out about how to cut into the lines for a parallel connection.
You want serial, so you you'll need a different approach.
There isn't a lot of room to work in. Like me, someone would have to use auto parts store hose sections to hook it up.