My situation as an example:
My historical hood is currently recovering from a plague (like a natural disaster?) and I ended up with rather many orphans and children the parents couldn't take care of and because it's a very populated I counted that I've over 40 children and young teens now (my sims's ages are somewhat modded, so realistically they are 5 to 15 years old) and more will end up there, and I'm pretty sure that most of them won't be able to find a new home via adoptions because most couples need to take care of their existing ones, or too sick/poor to adopt them. So now I try to scrambling up ideas what do with these sims when they are coming of age (in my age, that's 16 as its inspired by the 17-18th century where people seems to grow up faster, and orphans older than that, i.e. halfway through teen, will remain at their parents diseased lot - depending on their economy situation).

I know you can run monastery and convents, but ALL of my sims who are homo-sexual or a-sexual usually end up there (While I don't hate LGBT in real life, as I am a-sexual myself, my hood has that the same culture view from the past where it was more frowned upon), because same-sex couples are not acceptable in this hood I'm playing due to it's religious culture set up. ----- So I already have plenty of sims who will live at those institutes and the realism in me, it just feel weird to dump a group of teen sims with minimal education to live in a "normal" resident like if they were moved out from their family's house as they don't have any funds and limited when it comes to jobs.

You could have several of them form a gang and squat in an abandoned building, scraping by through begging or stealing. Do you have any Sims who need apprentices or will offer room and board in exchange for manual labor?

Omglo.
Apprentices for orphaned teens from a upper or middle class (medieval noble/ gentry/ bourgeois) sounds a good idea as they do receive some education (but not allowed to the highest ones, like medicine, especially not when they are so young). Sims for the lowest classes (mediveal workers, peasants/farmers, serfs/servants) will not receive education.

You don't need an education to apprentice at, say, a mill. And if the orphanage was run intelligently, the orphans didn't sit around all day eating their heads off. They were given practical educations, whether it involved growing crops to support the orphanage, being trained for domestic labor, sewing, or whatever. The adult running the orphanage would have connections among employers, and any orphan with a good relationship with any adult should be able to get a reference, even if the adult in question has no job to offer.

In the wake of an epidemic, there should be a labor shortage. Depending on circumstances, teens turned loose from the orphanage should be able to find jobs as day laborers, field hands, domestics, errand runners, etc. Some may be able to set up as small (very small!) businessmen. I'm not sure how you'd sim a crossing sweeper (kid with a broom clearing the muck out of the way of people crossing the street in exchange for tips), linkman (lighting the way for people traversing an unlighted city at night), rag picker, etc.; but they could dig for treasure and set up a market stall, sleeping under the counter. If the epidemic has wiped out any entire families, there may be abandoned property they can take over for their own use. Associations of former orphans banding together in mutual support groups would make sense - one member could stay "home" and take care of the domestic work while the others hustle, legally or illegally, for the necessities of life.

Some will never be more than beggars, some will turn to crime, some will be mercilessly exploited, and some will find a niche of their own in society. That's how it's always been for kids in The System.

The church in Acadie saw to it that orphans were provided with a small farm or dowry when they moved out. Sponsored by the church, the orphans were often better off than younger sons or daughters of large families!

Maybe they can be hired out to local farms and businesses. If they're recovering from a plague, labour's in short supply.