I want to understand some points :
Does using- SOA mean that I am using web services ? (or vice-verse?)
If I use web services with CXF, do I need an ESB ? what are the advantages of ESB like MULE in an architecture with web services ?
if I publish my web services in Java, does that means any client who has my WSDL can use my service, even if he/she uses .NET or something else than Java? Can ESB handle that?
Does using- SOA mean that I am using web services ? (or vice-verse?) - SOA is a concept and web service is an implementation of SOA. There can be many ways to implement it but the most common one is the web services.
ESB is a major component in you SOA. Its the main integration hub.
Following diagram will give you a more understanding about SOA and ESB. (Disclaimer : I work for WSO2 and this is one of the diagram that gives you a clear understanding about SOA and ESB)
http://4.bp.blogspot.com/_yO8q3CIhuZs/S-Zq88vkJlI/AAAAAAAAAak/QAJeDVXVL_4/s1600/wso1.png
If you are talking about web services, that means they are independent from programming language. Of course ESB can handle it and it can handle many other protocols as it is the integration hub.
Unfortunately, only the use of a specific technology is not a concrete evidence that you are doing SOA, as said in other response by Kasun Indrasiri, SOA is a concept, a technique that can be implemented using various tools from different vendors.
If you are designing services following the SOA Principles, you will be probably doing SOA, even if the tools you are using do not have all the features present in other modern platforms.
In my opinion, if your company does not have a of multi million dollars budget to spend on software licenses, you can still benefit from SOA using current tools.
