In this paper, we consider the problem of recovering desired sound source signals from on-board microphone recordings on a noisy drone.  Enhancement of source signal degraded by drone noise is considered to be a difficult task due to the strong noise generated from its motors and propellers causing an extremely low signal-to-drone noise ratio (SDNR).  We propose a solution (i) by using a multichannel Wiener filter (MWF) to remove drone noise from microphone recordings, and (ii) further reduction of residual noise using a Gaussian mixture model (GMM) based dual-stage parametric Wiener filter (WF).  The method exploits known statistics of motor current-specific drone noise.  The theory developed is applicable to irregular microphone arrays embedded on a drone enabling realistic integration to most drones. We demonstrate the validity of the proposed framework through (i) experimental recordings from two different drone acoustics datasets and (ii) outdoor measurements from a hovering drone for a bioacoustic application. The results confirm improved performance in terms of SDNR, speech quality (PESQ), and intelligibility (STOI) at very low SDNR levels (up to -30 dB) and show a strong potential for signal enhancement applications using noisy drones.