Mobile project development questions

Someone approached and asked me to develop a mobile application for iphone, blackberry, android and windows. My question is do I need to develop using different SDKs for each of the mobile? Secondly, is there a cross-platform tool I can use which code ones and works for all? If not, what is the easiest way for me to code for each of the platform. Please note, I do have programming knowledge and experience in C, C++ and C# and I also worked in Java, so learning is not a problem, but time to get the work done is what I'm looking for. Thank you

Each platform has different SDKs, APIs and programming languages (Java for Android, Objective-C for iOS, I'm not sure about Blackberry or Windows Phone).

However, there are actually some cross-platform tools that work by having you program your application using JavaScript and HTML. Your JS/HTML code then runs inside a browser control in a native app and a custom JavaScript API provides it with the functionality from the phone's native API. One example is Phonegap.

Is phonegap works on windows machine even for iOS development? What is the disadvantages of using phoneGap as opposed to a native SDK e.g. xcode for ios? I'm trying to get 100% right with the delivery of the solution to the client.