Why most non-invasive current sensors have a minijack at the other end?
Many Non invasive current sensors come without a minijack
The minijack is manufacturer specific. Use an amplifier made by the same manufacturer to convert the readout to something sensible (for example sparkfun sells this sensor, with this breakout board).
In the case of current transformers the output is a voltage that can be amplified and monitored with an ADC.