SrLaMnO4 is a layered antiferromagnetic (AF) oxide with the tetragonal (I4/mmm) n = 1 Ruddlesden Popper phase structure (also known as the K2NiF4 structure) with T-N = 128 K. Remarkably, substitution of Sr2+ by Ba2+, forming the solid solution Bai_xSrx.LaMnO4, results in the destruction of long-range magnetic order and of the ordered moment on Mn3+ for x > 0.35, although the effective paramagnetic moment remains unchanged, an unprecedented behavior for this class of magnetic materials. Four members, x = 0.0, 0.25, 0.35, and 1.0, have been studied using XYZ neutron polarization analysis which permits isolation of the magnetic, nuclear and nuclear spin components of the scattering and the measurement of the absolute value of the magnetic cross section. Data analysis is done using model independent reverse Monte Carlo methods (SPINVERT). The results for x = 0.0 (SrLaMnO4), T > TN(128 K), show an asymmetric diffuse peak which evolves into resolution limited Bragg peaks below TN and a fully ordered AF ground state with a Mn3+ moment of 3.06 ItB. For x = 0.25 the magnetic scattering below TN displays a remarkable phase separation Bragg reflections coexisting with diffuse scattering. The ordered Mn3+ moment is 1.1 ttB, much reduced from that obtained via unpolarized neutrons. There are no Bragg peaks for x = 0.35 at any measured temperature (T > 3 K) but there is highly structured diffuse scattering indicating strong short-range order reminiscent of x = 0 and 0.25 above their respective transition temperatures. For x = 1.00 (BaLaMnO4) the diffuse scattering roughly follows a paramagnetic form-factor indicating no short or long-range magnetic correlations. It is argued that the observed phenomena are due to a competition between AF and ferromagnetic (F) superexchange interactions for the 180 Mn3+-O Mn3+ geometry within the ab plane and that the changes in the local geometry of the Mn O octahedron leads to reduction of the AF interaction with a likely enhancement of the F interaction with increasing Ba content, ultimately giving rise to a glassy ground state. Analysis of the diffuse magnetic components show clear 2D AF spin correlations above TN for x = 0.00, 0.25, and 0.35 with correlation lengths, 14-7 A and no spin correlations for x = 1.00.