Can an ordinary transformer be used for coupling the speaker with a transistor amplifier
If your transformer has been adequately designed for power applications (50/60 Hz) it will make a poor audio transformer. Ask yourself the question - why does a transformer use laminations - did you know they are insulated from each other so that electrically they don't conduct?

Did you know that if they did all conduct you would have one massive shorted turn?

So, the laminations are there to prevent excessive shorted turns and the thickness might be (say) 1mm and suitable for 50/60 Hz - will that thickness laminate be suitable for 1 kHz - no. You'll get a lot of heating and wasted energy just fighting the eddy currents.

What about coupling factor - a power transformer has (with some hand waving) a coil coupling factor of about ~97%. An audio transformer is much closer to 100%, probably at least 99.5 %. Does this matter? It does at high frequencies because if you added a few tens of milli-henry external to your primary and tried to pass 20 kHz through it you wouldn't get a very good result. That's what happens with leakage inductance - it doesn't couple magnetically to the secondary. 

Consider a primary with inductance of 10 H - that's great for 230V AC but the leakage could be 3% of that at 300 mH. At 20 kHz, 300 mH has an impedance of about 38 kohm.

So, if you just want some "near-enough" crappy-fidelity thing with loss of top-end that's fine, use a power transformer.


  I measured the impedance using multimeter. For the primary side it is
  2 kilo-ohms and for the secondary, it is 11 ohms


Those are the dc resistances of the windings and that means your speaker on the secondary is in series with 11 ohms - a lot of power loss there if you have an 8 or 4 ohms speaker.