I agree with Hans that you should use a standard and well-tested library to do this. However, if you are writing a server to learn about HTTP, here's some info on doing what you want to do.
You really can't use a BufferedReader because it buffers the input and might read too many bytes from the socket. That's why your code is hanging, the BufferedReader is trying to read more bytes than are available on the socket (since the POST data doesn't have an end of line), and it is waiting for more bytes (which will never be available).
The process to simply parse a POST request is to use the InputStream directly
For each line in the header
read a byte at a time until you get a '\r' and then a '\n'
Look for a line that starts with "Content-Length: ", extract the number at the end of that line.
When you get a header line that is empty, you're done with headers.
Now read exactly the # of bytes that came from the Content-Length header.
Now you can write your response.