We report the interactions and dynamics of chemically powered soft swimmers that undergo autonomous oscillatory motion. The interaction of autonomous entities is the basis for the development of collective behaviors among biological organisms. Collective behaviors enable organisms to efficiently attain food and coordinate against threats. The basis of these behaviors is the interaction between nearest neighbors. Mimicking these interactions in artificial systems would enable their organization for the performance of complex tasks. Oscillatory phenomena are also ubiquitous in nature. Hence artificial oscillatory systems can serve as the most direct mimics and models of many biological systems. In this work, we report the interactions and dynamics of oscillatory swimmers propelled by the nonlinear oscillatory Belousov-Zhabotinsky (BZ) reaction. Individually, these swimmers displace by undergoing nonfully reciprocal oscillatory motion in conjunction with the BZ reaction. We find that, in addition to their individual oscillatory motion, multiple BZ swimmers exhibit successive oscillatory changes in their inter swimmer distance. This oscillatory attraction and repulsion between adjacent swimmers occurs in conjunction with the BZ waves and oxidation state of the catalyst. The effect of swimmer size and number on these dynamic interactions is interrogated. The level of chemical synchronization between multiple swimmers is determined. This work is a starting point for the design of collective behaviors utilizing autonomous chemically propelled soft swimmers.