Can intermediate frequency transformer be classified as a variable inductor ?
An IF transformer usually has two windings in it so it does contain variable inductors, but these may be tuned to a fixed frequency by placing capacitors across the inductors.
If you have two parallel tuned circuits close enough to each other, then they will pass energy between them but only at a very limited range of frequencies. Other frequencies are mostly rejected. A common IF frequency is 455 KHz.
IF transformers like that were mostly used for valve amplifiers because they had high impedance inputs and fairly high output impedances.
IF transformers for FETs can have a low impedance input winding and a tuned secondary. This has the advantage that there is a voltage step-up and a lot of the voltage gain of the amplifier can come from this step-up
What is its actual use in radio ?
A signal is mixed with an oscillator in a MIXER and the output of this will usually be the difference of the two frequencies. This will be a lower frequency than the input signal or the oscillator.
An IF amplifier is used then which is only tuned when the receiver is built. It amplifies signals at one frequency or small range of frequencies.
Between stages of this amplifier, there are IF transformers which actually provide the selectivity while the active device ie transistor, FET, Valve or IC provides the power gain.
You might like to read about superheterodyne receivers.
http://en.wikipedia.org/wiki/Superheterodyne_Receivers
http://upload.wikimedia.org/wikipedia/en/f/f1/Superhet2.png