We characterize blue straggler stars (BSSs) and yellow straggler stars (YSSs) of the open cluster (OC) Berkeley 39 using multiwavelength observations including the Swift/Ultraviolet and Optical Telescope (UVOT). Our analysis also makes use of ultraviolet (UV) data from Galaxy Evolution Explorer, optical data from Gaia DR3 and Panoramic Survey Telescope and Rapid Response System, and infrared data from Two Micron All Sky Survey, Spitzer/IRAC, and Wide-field Infrared Survey Explorer. Berkeley 39 is a ~6Gyr old Galactic OC located at a distance of ~4200pc. We identify 729 sources as cluster members utilizing a machine-learning algorithm, ML-MOC, on Gaia DR3 data. Of these, 17 sources are classified as BSS candidates and four as YSS candidates. We construct multiwavelength spectral energy distributions (SEDs) of 16 BSS and two YSS candidates, within the Swift/UVOT field, to analyze their properties. Out of these, eight BSS candidates and both the YSS candidates are successfully fitted with single-component SEDs. Five BSS candidates show marginal excess in the near-UV (NUV; fractional residual <0.3 in all but one UVOT filter), whereas three BSS candidates show moderate to significant excess in the NUV (fractional residual >0.3 in at least two UVOT filters). We present the properties of the BSS and YSS candidates, estimated based on the SED fits.