In quantum materials, basic observables such as spectral functions and susceptibilities are determined by Green's functions and their complex quasiparticle spectrum rather than by bare electrons. Even in closed many-body systems, this makes a description in terms of effective non-Hermitian (NH) Bloch Hamiltonians natural and intuitive. Here, we discuss how the abundance and stability of nodal phases is drastically affected by NH topology. While previous work has mostly considered complex degeneracies known as exceptional points as the NH counterpart of nodal points, we propose to relax this assumption by only requiring a crossing of the real part of the complex quasiparticle spectra, which entails a band crossing in the spectral function, i.e., a nodal spectral function. Interestingly, such real crossings are topologically protected by the braiding properties of the complex Bloch bands, and thus generically occur already in one-dimensional systems without symmetry or fine tuning. We propose and study a microscopic lattice model in which a sublattice-dependent interaction stabilizes nodal spectral functions. Besides the gapless spectrum, we identify nonreciprocal charge transport properties after a local potential quench as a key signature of nontrivial band braiding. Finally, in the limit of zero interaction on one of the sublattices, we find a perfectly ballistic unidirectional mode in a nonintegrable environment, reminiscent of a chiral edge state known from quantum Hall phases. Our analysis is corroborated by numerical simulations both in the framework of exact diagonalization and within the conserving second Born approximation.