I see advantages of getting JSON response and formatting in client side but are there any advantages by using JSON for form submission compared to normal submission?
It probably depends on your server side application. You are usually posting data to servers using POST, so how do you format underline data depends on how do you want for your server to process it. POST provides some form of key->value protocol, while in JSON you can put more than that. You can also transfer json using GET by placing it in url.
You must look on json as a way how data is written, while normal submission with POST should give you just a way how you transport data(of course you can abuse key->value feature of it for ordering your data).
There exists protocols on top of HTTP, that could help you define interface to your web application. One good example is RESTfull http://en.wikipedia.org/wiki/Representational_state_transfer
Specifically for submitting forms, I don't see any advanatages, POST was designed for this in a first place. There are cases where you want to transmit not only data from form, but also some metadata in this case json might help you by encoding form data(with metadata) in some json format, but at the end you will be still abusing POST for transferig this json data.
Hope I answered your question.