The recent phase-sensitive measurements in the superconducting phase of provide strong evidence for the triplet, chiral pairing symmetries, which endow the Cooper pairs with orbital angular momentum projections along the axis. In the absence of disorder such pairing can support both line and point nodes, and both types of nodal quasiparticles exhibit nontrivial topology in the momentum space. The point nodes, located at the intersections of the closed Fermi surfaces with the axis, act as the double monopoles and the antimonopoles of the Berry curvature, and generalize the notion of Weyl quasiparticles. Consequently, the phase should support an anomalous thermal Hall effect, the polar Kerr effect, in addition to the protected Fermi arcs on the and the surfaces. The line node at the Fermi surface equator acts as a vortex loop in the momentum space and gives rise to the zero-energy, dispersionless Andreev bound states on the surface. At the transition from the phase to the phase, the time-reversal symmetry is restored, and only the line node survives inside the phase. As both line and double-Weyl point nodes possess linearly vanishing density of states, we show that weak disorder acts as a marginally relevant perturbation. Consequently, an infinitesimal amount of disorder destroys the ballistic quasiparticle pole, while giving rise to a diffusive phase with a finite density of states at the zero energy. The resulting diffusive phase exhibits -linear specific heat, and an anomalous thermal Hall effect. We predict that the low-temperature thermodynamic and transport properties display a crossover between a ballistic thermal Hall semimetal and a diffusive thermal Hall metal. By contrast, the diffusive phase obtained from a time-reversal-invariant pairing exhibits only the -linear specific heat without any anomalous thermal Hall effect.