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For an O(N) symmetric scalar field theory with Euclidean action integral d^3x[1/2 |nabla phi|^2 + 1/2 r phi^2 + 1/4! u phi^4], where phi = (phi_1,...,phi_N)is a vector of N real field components, variational perturbation theory throughseven loops is employed for N = 0,1,2,3,4 to compute the renormalized value ofr/(N+2)u^2 at the phase transition. Its exact large-N limit is determined aswell. We also extend an earlier computation of the interaction-induced shiftDelta<phi^2>/Nu for N = 1,2,4 to N = 0,3. For N = 2, the results for the twoquantities are used to compute the second-order shift of the condensationtemperature of a dilute Bose gas, both in the homogenous case and for the widelimit of a harmonic trap. Our results are in agreement with earlier Monte Carlosimulations for N = 1,2,4. The appendix contains previously unpublishednumerical seven-loop data provided to us by B.Nickel.Comment: 19 page

Nonuniversal critical quantities from variational perturbation theory and their application to the Bose-Einstein condensation temperature shift