Pas la peine dans le serveur de changer le charset en réponse :

@Override
	protected void doPost(HttpServletRequest req, HttpServletResponse resp) throws ServletException, IOException {
		String mess = "";
		if (req.getParameter("mess") != null) {
			mess = req.getParameter("mess");
		}
		JSONObject laReponse = new JSONObject();
		laReponse.put("mess", "RECU:::" + mess);
		//resp.setContentType("text/html; charset=UTF-8");
		//resp.setContentType("application/json");
	    //resp.setCharacterEncoding("UTF-8");
		resp.getWriter().print(laReponse.toString());
	}

Côté client on peut modifier :

postDataBuilder.append("&mess=").append(URLEncoder.encode(params[1],"ISO-8859-15"));