Structural investigations (neutron diffraction and electron microscopy), as well as data on resistance, magnetization, and second harmonic of magnetization, are presented for $^{154}\mathrm{Sm}_{0.5}{\mathrm{Sr}}_{0.5}\mathrm{Mn}{\mathrm{O}}_{3}$ manganite. The neutron diffraction studies reveal a structural phase transition at ${T}_{\mathit{st}}\ensuremath{\approx}135\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ from a high-temperature $Pbnm$ space group to a mixture of two $Pbnm$ phases, which are coherently coupled by atomic positions but differ in cell parameters. Above ${T}_{\mathit{st}}$, this compound is a paramagnetic insulator. At room temperature, a strained and complex nanostructure state is observed in the high-resolution electron microscopy images. In the $Pbnm$ structure it is generated by the coexistence of twinning domains and a small deviation from orthorhombicity for a monoclinic structure. Below ${T}_{\mathit{st}}$, both structural phases begin to exhibit coherent Jahn-Teller distortions, which are different in the two phases. The structural transition is accompanied by the development of a magnetic ordering, so that the ground state is a mixture of ferromagnetism (F) and $A$-type antiferromagnetism (AF-$A$). The AF-$A$ order develops in the new low-temperature structural phase II, whereas the F moment is related to the high-temperature structure I. The several variants of the magnetic ordering are considered for phase I. A more physically justified scenario is that this phase does not possess an AF-$A$ component and exhibits F ordering with an F moment of $1.9(1)\phantom{\rule{0.3em}{0ex}}{\ensuremath{\mu}}_{B}∕\mathrm{Mn}$ at $1.5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. In this case, the AF moment of phase II is found to be $4.1(1)\phantom{\rule{0.3em}{0ex}}{\ensuremath{\mu}}_{B}∕\mathrm{Mn}$ at $1.5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. This unexpected result is attributed to the formation of ferromagnetic polarons in connection with a new electronic structure proposed for the AF-$A$ state. A metalliclike behavior is only observed below $50\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and is related to the F phase. The AF-$A$ phase is expected to be insulating. It can exhibit a short-range charge ordering that is observed by electron diffraction at $92\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. A field hysteresis of the second harmonic is found above ${T}_{C}\ensuremath{\sim}{T}_{N}\ensuremath{\approx}{T}_{\mathit{st}}$, which is associated with AF-$A$ regions in the paramagnetic matrix which possess a weak ferromagnetism.