To investigate the size effect on rock mechanical properties, laboratory tests were conducted on rock specimens with identical height-to-diameter ratios but varying diameters from the Anjihaihe Formation, Donggou Formation, and Chang-7 Member. These tests included wave velocity measurements, wave velocity anisotropy tests, and uniaxial/triaxial compression experiments. The influence of specimen size on rock strength and wave velocity characteristics was systematically investigated. The results indicate these as fouows. The wave velocities of the three lithologies show no size effect. The Anjihaihe Formation exhibits stronger wave velocity heterogeneity, while the Chang-7 samples display stronger wave velocity anisotropy. Empirical relationships between density and velocity were established for the three lithologies. The uniaxial compressive strength (UCS) exhibits a significant size effect, showing nonlinear attenuation with increasing specimen size. Theoretical models for the compressive strength size effect of the three lithologies were established, revealing the unique attenuation characteristics of sandy mudstones under constant height-to-diameter ratio conditions. The triaxial compressive strength (TCS) is positively correlated with confining pressure. Furthermore, under different confining pressures, the strength is consistently influenced by specimen size (size effect), and the relevant theoretical model demonstrates universality. Through a constant height-to-diameter ratio experimental design, the independent influence of diameter variation on the strength size effect of sandy mudstones is highlighted, the understanding of the size effect mechanism in heterogeneous rocks is deepened. It provides theoretical support for the stability assessment of oil and gas reservoir engineering.