We experimentally demonstrate a modulation format identification (MFI) and optical signal-to-noise ratio (OSNR) monitoring method for digital coherent receivers by using the specific features of received signals' density distributions in Stokes axes combined with deep neural networks (DNNs). The features of received signals' density distribution fitting curves in S1 and S2 axes depend on the signal's modulation format and OSNR. The proposed technique extracts the features of these fitting curves' first-order derivation for MFI and OSNR monitoring, in order to improve the probability of format correct identification and OSNR estimation accuracy. Experimental results for 28Gbaud/s polarization-division multiplexing (PDM) quadrature phase-shift keying (QPSK), PDM 8 quadrature amplitude modulation (PDM-8QAM), PDM-16QAM, and 21.5Gbaud/s PDM-32QAM signals demonstrate OSNR monitoring over back-to-back transmission with mean estimation standard errors (SEs) of 0.21dB, 0.48dB, 0.35dB and 0.44dB, respectively. The MFI results over back-to-back transmission show that 100% identification accuracy of all these four modulation formats are achieved at the OSNR values lower or equal to their respective 7% forward error correction (FEC) thresholds. Similarly, 100% identification accuracy also is obtained for PDM-QPSK, PDM-8QAM, PDM-16QAM, and PDM-32QAM after 2000km, 2000km, 1040km, and 400km standard single-mode fiber (SMF) transmission within practical optical power ranges launched to the fiber, respectively.