We report the magnetization and electrical resistivity measurements of LaFeAsO and oxygen deficiency LaFeAsOx prepared by solid-state reaction. Superconductivity at around 35 K and a giant diamagnetic contribution at a higher temperature have been observed in LaFeAsOx, while the parent LaFeAsO is non-superconducting. However, after subtracting the paramagnetic background magnetic contribution, the parent compound exhibits a very small superconductivity at low temperatures below T-c similar to 35. The ZFC/FC (zero-field and field cooled magnetization) curves for both samples exhibit apparent irreversibility. The susceptibility increases significantly at low fields. All these behaviors seem to be explained by considering the system consisting of micro-scale weak poly-crystallite magnets owing to the dipolar magnetic interactions among them and individual localized nanoscale magnetic regions within crystallites. Furthermore, we have obtained the critical current density and the pinning force as a function of the applied field using the conventional Beans model. We conclude that the observed superconductivity has a filamentary character based on the implication of the superconductivity properties analyses.