What is the tiniest, low-power, and efficient am transmitter?
There is probably no real answer to this question, as the 'smallest' is subjective.

What you are looking for is an RF Variable Gain Amplifier (RF VGA). A Google image search of 'FET Variable Gain Amplifier' yields this as one which is simple, need no -ve voltage bias and will probably work.

http://www.seekic.com/circuit_diagram/Automotive_Circuit/LM307_voltage_controlled_gain_amplifier_circuit.html

You might want to change the LM307 for something with some sort of guaranteed bandwidth of at least 3MHz.

You connect your oscillator (crystal or resonant circuit) ideally through a filter reduce harmonics then pass the resulting carrier sine wave to the VGA which drive the antenna.

If you can use FM rather than AM the circuit becomes simpler.  If you do as suggested and use the microphone you will need to use a capacitive 'condenser' microphone which might be difficult to get hold of these days. (Most have built in amplifiers which hide the capcaitive output and produce a voltage)
A capacitive modulated oscillator produces an FM output directly, which is why it is so simple.

An RF VCO is still simple to make, what you need is an RF Voltage Controlled Amplifier (RF VCO)

A google image search of "FET Voltage Controlled Oscillator" yields hundreds.

A good 'small one' one might be Question 9, here http://www.allaboutcircuits.com/worksheets/modulate.html

Obviously you need to choose the tank (resonant) circuit component to make it oscillate at 1.52Mhz