Could you supply a link to the record? Or give us a citation to it so we can locate it?

The person in question in your link, is Maja Katrina Zachrisdotter, b. 17 Sept. 1819 in Ölme. The move out column is the last column on the left-hand page. It says she has moved to "S. Tofta" in 1837. The notation in the last column of the right-hand page looks to read "Läste klent 1836" and I will have to ask @Ulrich Neitzel to give a translation of that. It may mean she can only read a little bit.

S(ödra) Tofta is a place (farm or village) in Ölme parish. Maja Katrina can be found here: https://sok.riksarkivet.se/bildvisning/C0039624_00012#?c=&m=&s=&cv=11&xywh=132%2C2307%2C2730%2C1434. This indicates that she moves to Södra Tofta from Lämås in 1837 and then moves back to Lämås in 1838.

You can find her still in Lämås in the 1841-1845 Household Examination records here: https://sok.riksarkivet.se/bildvisning/C0039625_00110#?c=&m=&s=&cv=109&xywh=235%2C207%2C3931%2C2066.

As far as your first question about Per Gustaf Söderstrom, the note to the far-right says that he becomes "engaged to M. O. dr. below". If you look 2 lines below Per's entry, you see Maja Olsdotter (b. 12 June 1809) and the note in the far-right column indicates that she becomes "engaged to Söderstrom above on 17 November 1837". That record can be found here: https://sok.riksarkivet.se/bildvisning/C0039652_00220#?c=&m=&s=&cv=219&xywh=451%2C3098%2C2981%2C1913.