Stress relaxation dynamics of entangled long-chain branched (LCB) polymers are investigated in small-amplitude oscillatory shear and following nonlinear step shear using model A(3)AA(3) multiarm (pom-pom) polymer liquids. A well-characterized multiarm 1,4-polybutadiene melt and its entangled solutions/blends with an unentangled linear 1,4-polybutadiene are the main focus of this study. Relaxation dynamics of multiarm polymers in oscillatory shear are found to be qualitatively similar to predictions of a recent theory for H-shaped polymers based on the tube model. On time scales longer than the relaxation time of the A arms, however, we find that relaxation dynamics of the multiarm polymer backbone A are more complex than predicted by this theory. Specifically, the backbone dynamics appear to be dominated by diffusive motion of the branch point in its original (undilated tube). This finding is inconsistent with expectations from theories based on the dynamic dilution ansatz. Stress relaxation dynamics of entangled A3AA3 polymers following nonlinear step shear are, paradoxically, simpler. For all polymers studied the nonlinear shear relaxation modulus G(gamma,t) equivalent to sigma(xy)(gamma,t)/gamma is factorable into separate time-dependent (G(t)) and strain-dependent (h(gamma)) functions. In every case, factorability is observed at times beyond a characteristic separability time t = lambda(k) that is comparable to the terminal relaxation time of the polymer. lambda(k) is also found to manifest a similar dependence on polymer solution concentration as the terminal time. At low shear strains (gamma < gamma(c) approximate to 5.5) and for t much less than lambda(k), the shear damping function of all A(3)AA(3) liquids is less strain softening than h(gamma) predicted by the Doi-Edwards theory. For higher shear strains and t much less than lambda(k), multiarm solutions with more than three entanglements per arm manifest a transition to more strain softening, Doi-Edwards-like, damping behavior. The strain gamma(c) at the transition is a weak function of t and is close to the theoretical estimate for branch point withdrawal in entangled A3AA3 molecules. At longer times (t greater than or equal to lambda(k)), no transition is observed, and the damping function is in fair accord with the Doi-Edwards theoretical prediction for entangled linear polymers over the entire range of shear strains studied. h(gamma) for multiarm polymer solutions with less than three entanglements per arm do not change slope at the critical strain and are quite similar to the damping function of entangled linear polymer solutions.