We consider an active, stochastic microscopic model of particles suspended in a fluid and show that the coarse-grained description of this model renders odd viscoelasticity. The particles are odd dumbbells, each featuring a robotic device as the bead, which exhibits a particular torque response. We show that this model can be macroscopically treated as a viscoelastic fluid, analytically calculate the coefficients of the corresponding viscoelastic model, and corroborate the results using molecular dynamics simulations. This study provides a unified analytical framework for several experimental and numerical setups designed to elucidate odd effects in fluids.