A giant linear magnetoelectric effect was observed by Y. Tokura's group recently in multiferroic DyFeO3, which demands a detailed investigation of its magnetic properties. Additionally, there is little information on the changes of chemical and physical properties of these materials with the reduction in particle size in spite of the potential applications of these materials in nanoscale devices. As the wet-chemical synthesis of these materials in nanosize and getting a control over crystallinity and stoichiometry is nontrivial and poses a serious challenge prohibiting the study of their size-dependent properties. Here, we report the synthesis of DyFeO3 nanoparticles using a surfactantless hydrothermal method with a detailed magnetic property measurement. The as-synthesized DyFeO3 nanoparticles showed excellent crystallinity with average particle size in the range 50-60 nm. The structural analysis indicated that they are of a distorted orthorhombic pervoskite crystal structure. Detailed dc magnetization measurements in the temperature range of 3-350 K could isolate the presence of Dy3+-Fe3+ and Dy3+-Dy3+ superexchange interactions, which showed up as spin reorientation transitions in various temperature regions due to the differing magnitude of their interactions resulting in continuous rotation of antiferromagnetic component of Fe3+ spins with cooling of the sample. Nanosized DyFeO3 showed spin-reorientation transitions near 315 and 70 K due to the Dy 3+-Fe3+ interaction accompanied with an opening up of the hysteresis loop followed by antiferromagnetic ordering around 4 K due to a possible Dy3+-Dy3+ interaction. We also observed significant effect of the particle size reduction on the magnetic properties. The main effects seen by us were in terms of (1) pronounced spontaneous spin reorientation transitions, (2) the absence of Morin transition, and (3) presence of temperature-dependent exchange bias in the DyFeO3 nanoparticles. We present a detailed mechanism to explain these features based on the interplay of Dy3+ and Fe3+ spins as well surface disorder, anisotropy, canting, and so forth.