Measurements of anisotropic flow coefficients (vn) and their cross-correlations using two- and multiparticle cumulant methods are reported in collisions of pp at s=13 TeV, p-Pb at a center-of-mass energy per nucleon pair sNN=5.02 TeV, Xe-Xe at sNN=5.44 TeV, and Pb-Pb at sNN=5.02 TeV recorded with the ALICE detector. The multiplicity dependence of vn is studied in a very wide range from 20 to 3000 particles produced in the midrapidity region |η|<0.8 for the transverse momentum range 0.2<pT<3.0 GeV/c. An ordering of the coefficients v2>v3>v4 is found in pp and p-Pb collisions, similar to that seen in large collision systems, while a weak v2 multiplicity dependence is observed relative to nucleus-nucleus collisions in the same multiplicity range. Using a novel subevent method, v2 measured with four-particle cumulants is found to be compatible with that from six-particle cumulants in pp and p-Pb collisions. The magnitude of the correlation between vn2 and vm2, evaluated with the symmetric cumulants SC(m,n) is observed to be positive at all multiplicities for v2 and v4, while for v2 and v3 it is negative and changes sign for multiplicities below 100, which may indicate a different vn fluctuation pattern in this multiplicity range. The observed long-range multiparticle azimuthal correlations in high multiplicity pp and p-Pb collisions can neither be described by pythia 8 nor by impact-parameter-Glasma, music, and ultrarelativistic quantum molecular dynamics model calculations, and hence, provide new insights into the understanding of collective effects in small collision systems.