Merging galaxy clusters often host spectacular diffuse radio synchrotron sources. These sources can be explained by a non-thermal pool of relativistic electrons accelerated by shocks and turbulence in the intracluster medium. The origin of the pool and details of the cosmic ray transport and acceleration mechanisms in clusters are still open questions. Due to the often extremely steep spectral indices of diffuse radio emission, it is best studied at low frequencies. However, the lowest frequency window available to ground-based telescopes (10-30 MHz) has remained largely unexplored, as radio frequency interference and calibration problems related to the ionosphere become severe. Here, we present LOFAR observations from 16 to 168 MHz targeting the famous cluster Abell 2256. In the deepest-ever images at decametre wavelengths, we detect and resolve the radio halo, radio shock and various steep spectrum sources. We measure standard single power-law behaviour for the radio halo and radio shock spectra and find significant spectral index and curvature fluctuations across the radio halo, indicating an inhomogeneous emitting volume. In contrast to the straight power-law spectra of the large-scale diffuse sources, the various AGN-related sources often show extreme steepening towards higher frequencies and flattening towards low frequencies. We also discover a new fossil plasma source with a steep spectrum between 23 and 144 MHz, with $\alpha=-1.9\pm 0.1$. Finally, by comparing radio and gamma-ray observations, we rule out purely hadronic models for the radio halo origin in Abell 2256, unless the magnetic field strength in the cluster is exceptionally high, which is unsupportable by energetic arguments and inconsistent with the knowledge of other cluster magnetic fields.