About the birth of Poul Erichsen, father of Theodor Paulsen (Theodore was Otto Braaten's father-in-law, which you obviously know. I post that for clarity not for information).
I am sorry I cannot have too much confidence in that birth in 1793. It seems the baby boy's father is Jens?
The marriage record for Poul Erichsen Torshoug and Johanne Torkildsdatter omits their ages and birth place and fathers, as you noted. Is it correct we have no known birth year and birth place for Poul?
There are at least three Poul Erichsen (spellings vary) in the 1801 census in Enebakk of the right age to get married in 1828, and he certainly could be born after 1801 and would not appear in that census. Only by finding him connected to Torshoug could a birth for him feel secure. A "Poul" born in Enebak is not enough to identify him. Try checking vaccination records, and confirmation records, and moving in records as a safeguard that he did not arrive from elsewhere (though those records are usually incomplete, at least not finding him would be some evidence he is local). His birth year could be 1780 - 1812, more or less. Look again (I haven't) for records for his children for clues (his age, possible relatives as godparents, etc.). Check the bygdebok for Enebakk. Check for a death and probate for him. You have an idea when and where he died (before 1865 in Enebakk). I expect it may be possible but cumbersome, maybe, to establish his identity/birth parents. Not sure your rationale for the birth record you posted, so maybe I missed the point! Certainly is hard to read the early records, as you say. There's a transcribed list of confirmands in Enebak I thought I saw online at one point - I don't have a link at hand.