Lack of proper supply decoupling also leads to instability. So does the OPAMP have at least 100n cap directly on its supply pins, and the whole circuit is decoupled with some electrolytic cap like a hundred micros?
And how did you get that 47k resistor in the base?
And as c4757p adviced, add Rbe resistors. About 100 ohms for 3055, a few kiloohms for the 3904 (not the best choice, BD139 should be more suitable, if you plan to draw more current from the output). The 47k resistor in the base must go out. No need for that, its jus too much big.
If you want to use that as a voltage regulator, you can also add some minimum capacitance on its output to increase stability.
When you get rid of oscillation (try also not to use too long wires to hook the power device), the nex step would be adding capacitance in parallel with the zener diode - it should decrease a little its noise voltage and increase PSRR performance. Also slows down the output voltage slope when powering on (depending on the capacity in parallel with the ZD).
You also wrote something about constant current. What? This circuit is not a current source, it is a voltage source. Placing a big base resistor there does not make it behave like a current source, but like a shit voltage source, because the opamp goes saturate rather quickly, so it cannot supply enough current to the base. So do you need a current or voltage source? This circuit is a voltage source. If you need to power leds directly, you need current source. That requires a little modification for the circuit. And no it is not a garbagge, it just need a little tweak. Also the modification for sroucing current is easy.