The interior of cellular nuclei, the nucleoplasm, is a crowded fluid that is pervaded by protein-decorated DNA polymers, the chromatin. Due to the complex architecture of chromatin and a multitude of associated non-equilbrium processes, e.g. DNA repair, the nucleoplasm can be expected to feature non-trivial material properties and hence anomalous transport phenomena. Here, we have used single-particle tracking on nuclear actin rods, which are important players in DNA repair, to probe such transport phenomena. Our analysis reveals that short actin rods in the nucleus show an intermittent, anti-persistent subdiffusion with clear signatures of fractional Brownian motion. Moreover, the diffusive motion is heterogeneous with clear signatures of an intermittent switching of trajectories between at least two different mobilities, most likely due to transient associations with chromatin. In line with this interpretation, hyperosmotic stress is seen to stall the motion of nuclear actin rods, whereas hypoosmotic conditions yield a reptation-like motion. Our data highlight the local heterogeneity of the nucleoplasm, e.g. distinct biochemical microenvironments and chromosome territories, that need to be taken into account for an understanding of nucleoplasmic transport and the mechanobiology of nuclei.