Improvements in magnetodielectric and multiferroic properties are essential for visualizing the real application of multiferroics, precisely, BiFeO₃ (BFO). An enhancement of multiferroic and magnetodielectric properties has been achieved for chemically prepared nanocrystalline BFO by virtue of  Sm doping. The X-ray diffraction study confirms the growth of single phase nanocrystalline BFO which corroborates TEM observation. The magnetic study delineates the ferromagnetic behavior of nanocrystalline Sm-doped BFO samples even at room temperature, which is absent in pristine samples. Surprisingly, a few orders of magnitude increase in resistivity is observed in Sm doped samples. Room temperature ferroelectric measurement showed that Sm doping improves the polarization significantly. In addition, we have achieved a giant change in the magnetodielectric properties of Sm doped samples which has not been reported so far. Large lattice strain arising due to the mismatch of ionic radii and the decrease of oxygen vacancies combined could play an important role in the enhancement of multiferroic properties of nanocrystalline Sm-doped BFO which is a promising multiferroic material.