We present a lattice QCD study of charmonium resonances and bound states with JPC = 1(--) and 3(--) near the open-charm threshold, taking into account their strong transitions to (D) over barD. Vector charmonia are the most abundant in the experimentally established charmonium spectrum, while recently LHCb reported also the first discovery of a charmonium with likely spin three. The (D) over barD scattering amplitudes for partial waves l = 1 and l = 3 are extracted on the lattice by means of the Luscher formalism, using multiple volumes and inertial frames. Parametrizations of the scattering amplitudes provide masses and widths of the resonances, as well as the masses of bound states. CLS ensembles with 2 + 1 dynamical flavors of nonperturbatively O(a) improved Wilson quarks are employed with m(pi) similar or equal to 280 MeV, a single lattice spacing of a = 0.09 fm and two lattice spatial extents of L = 24 and 32. Two values of the charm quark mass are considered to examine the influence of the position of the (D) over barD threshold on the hadron masses. For the lighter charm quark mass we find the vector resonance psi(3770) with mass m = 3780(7) MeV and coupling g = 16.0((+2.1)(-0.2)) (related to the width by Gamma = g(2)p(3)/6 pi m(2)). Both quantities are consistent with their experimental values, m(exp) = 3773.13(35) MeV and g(exp) = 18.7(9). The vector psi(2S) appears as a bound state with m = 3666(10) MeV. The charmonium resonance with J(PC) = 3(--) is found at m = 3831((+10)(-16)) MeV, consistent with the Xo3842+ recently discovered by LHCb. At our heavier charm-quark mass the psi(2S) as well as the psi(3770) are bound states and the Xo3842+ remains a resonance. We stress that all quoted uncertainties are only statistical, while lattice spacing effects and the approach to the physical point (for the light and strange quarks) still need to be explored. This study of conventional charmonia sets the stage for more challenging future studies of unconventional charmoniumlike states.