To draw Venn diagrams in Stata you will need the user-written command venndiag, which can be downloaded from SSC with the following command in Stata:
ssc install venndiag

To generate this graph in Stata, use the following commands:
clear
input hayfever eczema asthma freq
1 0 0 31088
1 1 0 9863
0 1 0 43522
0 1 1 9258
0 0 1 35299
1 0 1 11024
1 1 1 6200
0 0 0 345262
end
list
expand freq
venndiag asthma eczema hayfever
For a comprehensive exploration of the many Stata graph commands and options, check out the book A Visual Guide to Stata Graphics, 3rd Edition.