We investigate the conformations of DNA-like stiff chains, characterized by contour length (L) and persistence length (l(p)), in a variety of crowded environments containing mono-disperse soft spherical (SS) and spherocylindrical (SC) particles, a mixture of SS and SC, and a milieu mimicking the composition of proteins in the Escherichia coli cytoplasm. The stiff chain, whose size modestly increases in SS crowders up to phi approximate to 0.1, is considerably more compact at low volume fractions (phi <= 0.2) in monodisperse SC particles than in a medium containing SS particles. A 1:1 mixture of SS and SC crowders induces greater chain compaction than the pure SS or SC crowders at the same phi, with the effect being highly nonadditive. We also discover a counterintuitive result that the polydisperse crowding environment, mimicking the composition of a cell lysate, swells the DNA-like polymer, which is in stark contrast to the size reduction of flexible polymers in the same milieu. Trapping of the stiff chain in a fluctuating tube-like environment created by large-sized crowders explains the dramatic increase in size and persistence length of the stiff chain. In the polydisperse medium, mimicking the cellular environment, the size of the DNA (or related RNA) is determined by L/l(p). At low L/l(p), the size of the polymer is unaffected, whereas there is a dramatic swelling at an intermediate value of L/l(p). We use these results to provide insights into recent experiments on crowding effects on RNA and also make testable predictions.