In addition to what Nick said and just some FYI:
The Graphic card with it's own GPU processor runs the screen output. The 256MB on the card is to help the GPU process the images you see. The larger that number is the more "room" the GPU has to manipulate the output data. If the GPU does not have enough "room" it will use some of the computer's system memory.
I have a lot of extensive experience with PCs and I have never used and external Graphics card. That card needs and works best when attached to the motherboard(PC)/logic board(Mac) to be fast and effective. The use of a Thunderbolt box with a 2008 Macbook would not be cost effective and would not give you the results you want.
As to internal storage - which is your hard drive that holds all your apps and data - yes, that can be updated. I have a 2009 Macbook and I have updated the system memory and installed a SSD drive. It breathed new life into an old mac. Keep in mind whatever upgrades you make you still are working with a 2008 logic board that has it's limits too.
So if you are trying to get better performance out of a 2008 Macbook Pro the options are to upgrade the system memory and change out the hard drive with a new SSD drive. If that is what you are looking for post back your questions and either I or Nick can make recommendations. Keep in mind it is an older machine and you need to consider what it is worth versus a new computer.
Also check out
ifixit.com. That may help give you a picture of what is possible.
Lisa