I use GZIPOutputStream or ZIPOutputStream to compress a String (my string.length() is less than 20), but the compressed result is long
Huffman encoding is a sensible option here. Gzip and friends do this, but the way they work is to build a Huffman tree for the input, send that, then send the data encoded with the tree. If the tree is large relative to the data, there may be no not saving in size.
However, it is possible to avoid sending a tree: instead, you arrange for the sender and receiver to already have one. It can't be built specifically for every string, but you can have a single global tree used to encode all strings. If you build it from the same language as the input strings (English or whatever), you should still get good compression, although not as good as with a custom tree for every input.