The semicolon tells sed to do exactly what it is doing, search for this and do what I tell you to, then once that is complete here is the next string. I'm not going to be the one but if you simply switch the order of your strings you would avoid your second search picking up the string1's that were changed to string2.
So you do
sed -e 's/string2/string3/g;s/string1/string2/g' /file > /new_file
And yes there are other ways to do this and we could go into deeper talk about alternatives but this is easy. If you want more info just ask.