The VennDiagram package is very useful for making and preparing VennDiagrams but you have to know the values of the overlaps. It will make Venn and Euler Diagrams.
To calculate the overlaps between your groups you can download other packages but it's actually pretty simple with normal R code.
The intersect() function will give you the number of elements that are the same in two vectors.
The setdiff() function will give you the number of elements in one vector but not the other.
These are all detailed in the Set Operation page and there is a useful StackOverload answer too.
So the basic script you need to write has the following elements:
(1) Read in the csv file - function - read.csv()
(2) Turn your data into three vectors - function - as.vector()
(3) Compare your sets using the intersect() and setdiff() functions.
(4) Draw your Venn or Euler diagram with the VennDiagram package
If you want to use a package to give you the overlaps from the lists you can try gplots (http://cran.r-project.org/web/packages/gplots/vignettes/venn.pdf).
I have written a script about comparing two protein lists that is a simplified version of what you're trying to do.
I hope this helps. Good luck, P