We present the results of a lattice calculation of tetraquark states with quark contents q(1)q(2)(Q) over bar(Q) over bar, q(1), q(2) subset of u, d, s, c and Q equivalent to b, c in both spin-0 (J = 0) and spin-1 (J = 1) sectors. This calculation is performed on three dynamical N-f = 2 + 1 + 1 highly improved staggered quark ensembles at lattice spacings of about 0.12, 0.09, and 0.06 fm. We use the overlap action for light to charm quarks, while a nonrelativistic action with nonperturbatively improved coefficients with terms up to O(alpha(s)v(4)) is employed for the bottom quark. While considering charm or bottom quarks as heavy, we calculate the energy levels of various four-quark configurations with light quark masses ranging from the physical strange quark mass to that of the corresponding physical pion mass. This enables us to explore the quark mass dependence of the extracted four-quark energy levels over a wide range of quark masses. The results of the spin-1 states show the presence of ground state energy levels which are below their respective thresholds for all the light flavor combinations. Further, we identify a trend that the energy splittings, defined as the energy difference between the ground state energy levels and their respective thresholds, increase with decreasing the light quark masses and are maximum at the physical point for all the spin-1 states. The rate of increase is, however, dependent on the light quark configuration of the particular spin-1 state. We also present a study of hadron mass relations involving tetraquarks, baryons, and mesons arising in the limit of infinitely heavy quarks and find that these relations are more compatible with the heavy quark limit in the bottom sector but deviate substantially in the charm sector. The ground state spectra of the spin-0 tetraquark states with various flavor combinations are seen to lie above their respective thresholds.