Well, it borrows a lot from python, has lisp-like macros, and has pretty good FFI to C. I don't think it has any network building or game libraries. There might be some web packages. It is mainly geared towards scientific computing.
Not sure quite what you mean by network building, but IO/networking is libuv-based so should be pretty good. There is TCP client/server functionality built into the language and UDP is coming soon.
As far as web, there is http://juliawebstack.org/.
None of this is polished yet and there is still a decent amount of work to be done on the core language. Additionally, since Julia is targeted for technical computing, the standard library includes linear algebra support and requires BLAS, which is great unless you don't need it and are on a system with memory constraints or want to incorporate Julia into another application, although there has been talk of decoupling the linear algebra support from the rest of the language. But yes, Julia the language should be suitable for all of these purposes.