Nonplanar penta-graphene and planar phagraphene, which are connected by carbon pentagons and penta-hexa-hepta carbon rings, respectively, are two allotropes of graphene. Graphene as a star material in two-dimensional materials has been widely studied. However, the studies around penta-graphene and phagraphene are still insufficient. We are interested in both materials' response to temperature, hydrostatic pressure, and stress. In this work, the thermal expansion, linear compressibility, and Poisson's ratio of penta-graphene and phagraphene have been investigated systematically. It is found that both materials can exhibit abnormal negative thermal expansion behavior, while their linear compressibility behavior is normal. The negative Poisson's ratio behavior only occurs in penta-graphene, which is consistent with other work. Through an analysis of the lattice vibrations and associated mode Grüneisen parameters, it is found that there are anomalies in the phonon spectra of both penta-graphene and phagraphene. It is noted that acoustic phonons contribute most to their respective anomalies, especially the transverse acoustic mode. The librational motion of the lowest-frequency optical phonon of both materials is identified and also associated with their novel properties. In general, the unique topological arrangement of carbon atoms can play a decisive role in determining the performances of penta-graphene and phagraphene.