A problem searching Hedmark parish registers

One of my ancestors, a certain Ole Olsen, lived in Løten, Hedmark, from around 1780 until around 1840. The only documentation I have found for him is his marriage in April 1812 in the Løten parish register (Ministerialbok). It lists his name, the farm he lived on, and the fact that he was born in Elverum. The Løten parish books at that time did not record the groom's age or his father's full name. I have also located the birth records for a couple of his children (born in 1812 and 1832). I have not yet found his death recorded, but am hopeful that I will eventually find it -- and from that I should be able to get the approximate year of his birth. I do know that his wife was born in 1786. I would like to track down the date and place in Elverum of Ole Olsen's birth, and his parents. However, the parish books in Løten and Elverum at this time did not contain the Innflyttede and Utflyttede (arrivals and departures). Nor did they record the place of birth, in the confirmation lists. Does anyone have advice on how to proceed? In particular, I'd be interested in suggestions of what to do in case I am not able to locate his death record in Løten. This would be easier if he had a name that was less common that "Ole Olsen"!