Born in Filovci to a minor noble family, Oslay attended elementary school in Puconci and received further education in Budapest. Oslay studied the Slovene March (Prekmurje) and contributed to Sándor Mikola's irredentist publication Domovina. Oslay's research topics were the history of Prekmurje, the local language, the Reformation, and Croatian history. Oslay made many claims that are untenable and unproveable, including that Styria was inhabited by Hungarians, and therefore Styria is also an ancient Hungarian area, or that the Slovenes in Prekmurje and Styria are assimilated Hungarians. Oslay supported the anti-Slavic chauvinistic propaganda of Sándor Mikola after World War I.