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We propose 2D Piezoelectric FET (PeFET) based compute-enabled non-volatile memory for ternary deep neural networks (DNNs). PeFETs consist of a material with ferroelectric and piezoelectric properties coupled with Transition Metal Dichalcogenide channel. We utilize (a) ferroelectricity to store binary bits (0/1) in the form of polarization (-P/+P) and (b) polarization dependent piezoelectricity to read the stored state by means of strain-induced bandgap change in Transition Metal Dichalcogenide channel. The unique read mechanism of PeFETs enables us to expand the traditional association of +P (-P) with low (high) resistance states to their dual high (low) resistance depending on read voltage. Specifically, we demonstrate that +P (-P) stored in PeFETs can be dynamically configured in (a) a low (high) resistance state for positive read voltages and (b) their dual high (low) resistance states for negative read voltages, without afflicting a read disturb. Such a feature, which we name as Polarization Preserved Piezoelectric Effect Reversal with Dual Voltage Polarity (PiER), is unique to PeFETs and has not been shown in hitherto explored memories. We leverage PiER to propose a Strain-enabled Ternary Precision Computation-in-Memory (STeP-CiM) cell with capabilities of computing the scalar product of the stored weight and input, both of which are represented with signed ternary precision. Further, using multi word-line assertion of STeP-CiM cells, we achieve massively parallel computation of dot products of signed ternary inputs and weights. Our array level analysis shows 91% lower delay and improvements of 15% and 91% in energy for in-memory multiply-and-accumulate operations compared to near-memory design approaches based on SRAM and PeFET respectively. STeP-CiM exhibits upto 8.91x improvement in performance and 6.07x average improvement in energy over SRAM/PeFET based near-memory design.