This paper evaluates the strain-sensing ability of a nanoengineered hierarchical twill weave composite using multiscale numerical simulations. Piezoresistivity is incorporated in such composite by introducing carbon nanotubes (CNT) in the polystyrene (PSS) matrix so as to form a percolating microstructure. The glass fiber twill weave, which itself contains CNT-modified PSS matrix inside the yarns, is coated with thin film of such piezoresistive matrix to obtain the smart composite configuration. The methodology, presented in this paper, captures the hierarchical intricacies at multiple length scales and implements various mechanical damage mechanisms at subsequent interactive length scales as well as consequent electrical responses so as to yield macroscopic electromechanical response. The simulated responses show excellent correlation with experimental observations signifying the efficacy of the simulation methodology. Such a detailed multiscale approach can provide valuable insights towards tuning of structural hierarchies at multiple length scales for efficient design of smart woven laminated composites.