Magnetoacoustic emission (MAE) and Barkhausen emission (BE) have been measured as a function of applied magnetic field and tensile stress from mild-steel samples in a wide range of heat treatments, to develop a technique to measure stress without prior knowledge of the microstructure. The results are supplemented by measurements of magnetic coercivity and mechanical hardness. MAE is found to decrease with increasing applied stress, whereas the variation of BE is more complicated. The amplitudes of both MAE and BE, as well as the coercivity and hardness are also found to depend on the microstructure to varying degrees. Thus in ferritic-pearlitic and ferritic-pearlitic-martensitic steel MAE is much more sensitive to stress than to changes in microstructure, whereas the sensitivity of BE to stress and microstructure is similar. Above 50 MPa MAE is also more sensitive to stress in ferrite containing cementite, whereas BE both lacks a monotonic dependence upon stress and is sensitive to microstructure. In martensite, however, there is no MAE, the BE increasing monotonically with stress. Tempered martensitic structures give a weak MAE signal that is more sensitive to tempering temperature than applied stress, whereas the BE increases with stress for tempers below 500 $^\circ$C and decreases above. The dependence of MAE and BE on magnetic field are discussed in terms of domain-wall nucleation and irreversible motion in ferrite at higher fields, and irreversible wall motion through martensite or pearlite at lower fields. The results imply that MAE can be used alone to measure stress provided the general form of the microstructure is known; otherwise BE can be used as an additional technique to resolve any ambiguity.