Using density functional theory calculations, we study the response of three representative graphene allotropes (two pentaheptites and octagraphene) as well as graphene, to uniaxial strain up to their fracture limit. Those allotropes can be seen as distorted graphene structures formed upon periodically arranged Stone-Walles transformations. We calculate their mechanical properties (Young\'s modulus, Poisson\'s ratio, speed of sound, ultimate tensile strength and the corresponding strain), and we describe the pathways of their fracture. Finally, we study strain as a factor for the conversion of graphene into those allotropes upon Stone-Walles transformations. For specific sets of Stone-Walles transformations leading to an allotrope, we determine the strain directions and the corresponding minimum strain value, for which the allotrope is more favorable energetically than graphene. We find that the minimum strain values which favor those conversions are of the order of 9-13%. Moreover, we find that the energy barriers for the Stone-Walles transformations decrease dramatically under strain, however, they remain prohibitive for structural transitions. Thus, strain alone cannot provide a synthetic route to these allotropes, but could be a part of composite procedures for this purpose.