Two-particle Azimuthal correlations are measured with the ALICE apparatus in pp collisions at s=13 TeV to explore strangeness- and multiplicity-related effects in the fragmentation of jets and the transition regime between bulk and hard production, probed with the condition that a strange meson (KS0) or baryon (Λ) with transverse momentum p_T> 3 GeV/c is produced. Azimuthal correlations between kaons or Λ hyperons with other hadrons are presented at midrapidity for a broad range of the trigger (3<pTtrigg<20 GeV/c) and associated particle p_T (1 GeV/c<pTassoc<pTtrigg), for minimum-bias events and as a function of the event multiplicity. The near- and away-side peak yields are compared for the case of either KS0 or Λ (Λ ¯) being the trigger particle with that of inclusive hadrons (a sample dominated by pions). In addition, the measurements are compared with predictions from PYTHIA 8 and EPOS LHC event generators.