For typical jet engines overall efficiency ranges from 20 to 40%. A very tiny fraction of a percent goes to generate noise. The vast majority of the energy not used for propulsion is wasted as heat. Jet engine efficiency calculation is very complicated and depends on a lot of things such as the speed, altitude, and temperature of the air. In general, efficiency is better at high altitudes, and high speeds. Also there are many kinds of efficiency: propulsive, heat, fuel, etc. For details on how all this is calculated try this Chapter from a book at NASA or this page from a report by the Intergovernmental Panel on Climate Change, especially figure 7.12 which shows how engines have improved over time, and how the Boeing 777's GE90-115B engine is the most efficient one in common usage today with efficiencies of about 37%. Experimental engines on the horizon may reach efficiencies of nearly 50%. For comparison, modern automobile engines are around 25% with a finely tuned diesel capable of achieving 32% efficiency.
A good source for the efficiency of particular engine types is Design of High-Efficiency Turbomachinery and Gas Turbines, by David Gordon Wilson, MIT Press, 1984, ISBN 0-262-23114-X, Chapter 3.