It depends on what you're trying to learn.
A lot of web vulnerabilities are completely independent of the underlying code, at least from the browsers perspective.
So
you should know enough with your skillset - I'd concentrate on understanding the vulnerabilities from the browser and/or server side without worrying about the server side languages.
They are important for some vulnerabilities, but I'd start with the generic ones (SQL injection, XSS etc) first.
If you want to learn how to prevent such vulnerabilities then definitely learn as much as possible about the languages that you will use.
FYI I know Java very well, HTML 5 / Java script etc fairly well (but have loads to learn), I can get by in Python, Perl, Struts, Hibernate but have very little knowledge of DotNet, Ruby and other languages.
Theres always too much to learn ;)
Cheers,
Simon