I have a party of 8 players, and more continue to join (against my wishes). How would you recommend challenging low-level (4 or lower) players that are in a large group? How do I give everyone a chance to be in the spotlight without rushing through or ruining some stories?
Large parties can be diffcult to run for any DM. You have a couple options to deal with this.
Force split the party
Pitfall traps, haunted houses with secret rotating doors, dopplegangers inflitrating the party, Magic maze, etc. By dividing the group, they can handle a lot less at once. This allows you to use creatures such as goblins, zombies and other lower CR monsters that a large party of even low level characters would normally step on as well as make sure each player gets to do something in a combat or have time to shine in a RP session.
As the party levels up, especially with 8 or more players, they will be able to take down higher CR monsters much quicker than a normal sized party of 4 or 5. Or you can send more creatures their way at one time. Orc war bands, gangs of Grimlocks, etc. Dropping characters is not the same as killing them, with 8 party mates someone is bound to be able to do some sort of healing. 5e is very forgiving with its death saves and low chances of insta death, keep in mind your players do have the option to run when things are tough, so don't be afraid to gauge their strength and reward good teamwork.
I have a party of 8 players and more continue to join (against my wishes).
This is concerning to me as you are the DM. Ultimately, you can only handle so much. I don't know your situation but extra players joining eithout the consent of the DM is INCREDIBLY rude. You have to work hard to make sure everyone is having a good time. You have the right to cap off a campaign. If it gets too full then no one will have a good time. Perhaps these new people can play if and when you start a new campaign, or have another game going among themselves. To be blunt, if your game is full, say it's full and be firm.
Balancing is always tricky with large groups.
In such a large party i would separate them in smaller groups. Like a secret wall in a dungeon, pulling some of them to another room, or something like that.
If you choose to compensate in numbers (+ foes, -hp), you are at risk of some characters outshinning others because of large dmg bursts causing "one hit kills"(we are looking at you, paladin with divine smite) and also, you will have a combat that would make Snyder's cut seem like a short movie.
I would make them fight a NPC with HUGE ammount of HP, multiattack and some legendary actions to be successful in saves. If you feel that he's being overwhelmed too easily, you could make him summon some minions or give him a regeneration trait.
You could also give them a buff in temporary hitpoints (a blessing, a powerful ally, a mysterious scroll). That would make less likely they die, while still mantaining the sense of danger and damage.
But personally, i would try to convince them that is not a good idea to have such a large party. Stealth would be penalized (a small crowd entering a dungeon would hardly pass unnoticed), the combats will take ages, the xp will be miserable, the social interactions will be chaotic...