What is the difference between web
service, web methods and server side
code ?
A web service is an exposed end point that is normally used as an API, or in other words its end user is typically another application rather than a user interface. A web method is a particular method that is exposed over a web service.
On the other hand, server-side code applies to any ASP.NET web page, web service, or other technology for general implementation of its functionality.
Where is web service preferred over
server side methods?
Web services excel at making an application compatible with other programming platforms or for serving up AJAX requests to a web page. There are many other uses, but typically using WCF or HttpHandlers are better options in those cases.
Where are web methods preferred to be
used ?
Web methods can be used in any .aspx page or more typically in a .asmx (web service) file.
How does web service differ from
server side post back ?
A server-side postback occurs when a web page posts data to the server for processing. A web service is completely different - it is an endpoint that is exposed for consumption by another application (or within the same application).
Are web services light weight ? Can
they be used to save long web forms as
well ?
No, web services are not light weight, in fact they are quite the opposite because they generally receive and respond to data using XML (a bulky format). However, this makes them very easy to use with other programming languages.
In an enterprise web application,
which one of these should I use
frequently and why?
This is a highly subjective question. Each technology in the .NET framework has a set of features that it excels at and can usually do several other things (but not very well). Each tool has its place, it is just a matter of matching the tools to use with the requirements of your project.
However, judging by the rest of your questioning, it sounds like you are just putting together a typical website that doesn't require an API, in which case it would be best to use .aspx pages and code behind.
