Apache HTTP Client was the first networking library used in Android. It has been deprecated in favor of HTTPUrlConnection. You can read more about it in this article.
HTTPUrlConnection is the new Android-approved networking library. You can read more about it in this article.
Retrofit makes all your network requests look like Java, simplifying the need to write an AsyncTask or Thread to manage your request and all of the parsing when you receive it.
OkHttp is the HTTP Client that is automatically used for these requests. You can use it as a standalone if you desire. It simplifies retry logic and removed the need to write your own AsyncTask's to manage concurrency.
Volley was introduced at Google I/O 2013. It allows you to handle network requests asynchronously - obviating the need for network AsyncTask's (through you may still want to use them when interacting with the file system/DB).
It's not straight forward to integrate since you need to build your own version of the jar and manually manage the versioning of that jar. You can use maven to help with that effort.