We analyse new observations with the International Low Frequency Array (LOFAR) telescope, and archival data from the Multi-Element Radio Linked Interferometer Network (MERLIN) and the Karl G. Jansky Very Large Array (VLA). We model the spatially resolved radio spectrum of Arp 220 from 150MHz to 33GHz. We present an image of Arp 220 at 150MHz with resolution 0.65"x0.35", sensitivity 0.15mJy/beam, and integrated flux density 394+/-59mJy. More than 80% of the detected flux comes from extended (6"~2.2kpc) steep spectrum (alpha=-0.7) emission, likely from star formation in the molecular disk surrounding the two nuclei. We find elongated features extending 0.3" (110pc) and 0.9" (330pc) from the eastern and western nucleus respectively, which we interpret as evidence for outflows. The extent of radio emission requires acceleration of cosmic rays far outside the nuclei. We find that a simple three component model can explain most of the observed radio spectrum of the galaxy. When accounting for absorption at 1.4GHz, Arp 220 follows the FIR/radio correlation with q=2.36, and we estimate a star formation rate of 220M_{sun}_/yr. We derive thermal fractions at 1GHz of less than 1% for the nuclei, which indicates that a major part of the UV-photons are absorbed by dust. International LOFAR observations shows great promise to detect steep spectrum outflows and probe regions of thermal absorption. However, in LIRGs the emission detected at 150MHz does not necessarily come from the main regions of star formation. This implies that high spatial resolution is crucial for accurate estimates of star formation rates for such galaxies at 150MHz.