Voltage control of the magnetic properties of oxide thin films is highly appealing to enhance energy efficiency in miniaturized spintronic and magnetoelectric devices. Herein, magnetoelectric effects in electrolyte-gated nanoporous iron oxide films are investigated. Highly porous films were prepared by the evaporation-induced self-assembly of sol-gel precursors with a sacrificial block-copolymer template. For comparison, films with less porosity but analogous crystallographic structure were also prepared using an identical procedure except without the polymer template. The films were found to be 70-85 nm in thickness as measured by scanning electron microscopy and primarily hematite as determined by Raman spectroscopy. The templated (highly porous) films showed a very large magnetoelectric response with a maximum increase in magnetic moment at saturation of a factor of 13 and a noticeable (2-fold) increase of coercivity (after applying -50 V). The nontemplated films also exhibited a pronounced increase of magnetic moment at saturation of a factor of 4, although the coercivity remained unaffected over the same voltage range. Magnetoelectric effects in these latter films were found to be fully reversible in the voltage window ±10 V. The observed changes in magnetic properties are concluded to be magneto-ionically driven with oxygen ion exchange between the iron oxide and the liquid electrolyte, as evidenced from Raman and X-ray photoelectron spectroscopy experiments.