According to the recent 3GPP decisions on 6G air interface, orthogonal frequency-division multiplexing (OFDM)-based waveforms are the primary candidates for future integrated sensing and communication (ISAC) systems. In this paper, we consider a monostatic sensing scenario in which OFDM is used for the downlink and its reflected echo signal is used for sensing. OFDM and discrete Fourier transform-spread OFDM (DFT-s-OFDM) are the options for uplink transmission. When OFDM is used in the uplink, the power difference between this signal and the echo signal leads to a power-domain non-orthogonal multiple access (PD-NOMA) scenario. In contrast, adopting DFT-s-OFDM as uplink signal enables a waveform-domain NOMA(WD-NOMA). Affine frequency-division multiplexing (AFDM) and orthogonal time frequency space (OTFS) have been proven to be DFT-s-OFDM based waveforms. This work focuses on such a WD-NOMA system, where AFDM or OTFS is used as uplink waveform and OFDM is employed for downlink transmission and sensing. We show that the OFDM signal exhibits additive white Gaussian noise (AWGN)-like behavior in the affine domain, allowing it to be modeled as white noise in uplink symbol detection. To enable accurate data detection performance, an AFDM frame design and a noise power estimation (NPE) method are developed. Furthermore, a two-dimensional orthogonal matching pursuit (2D-OMP) algorithm is applied for sensing by iteratively identifying delay-Doppler components of each target. Simulation results demonstrate that the WD-NOMA ISAC system, employing either AFDM or OTFS, outperforms the PD-NOMA ISAC system that uses only the OFDM waveform in terms of bit error rate (BER) performance. Furthermore, the proposed NPE method yields additional improvements in BER.