We played without Immunity to Normal Weapons, which was a mistake from our side (SR5 description should include Immunity to Normal Weapons since this is what Possession gives them), and took a rough guideline of 2 Shedim per player, since Missions are balanced on 6 players and a dozen vs six means 2 per 1.
At 9 Shedim vs 5 players, and a sudden "okay, you're nearby spying but now you roll Sneaking, someone fails so combat starts" bombshell, we took a bit of damage, especially the Mage. Auslander had 2 Shedim with him, with Immunity he clearly should be by himself, and even then our mage overcasting was part of how we got to kick his ass. Note that his Spell Defense should have applied here and ruined the aim of the AoE spell, but it was overcast at a level where that simply would have meant "Auslander, his minions AND several players take damage."
-----
BALANCING TRICKS
1: You got a party of 4, so I'd give them a tough fight and throw 8 Shedim at them. If they're smart, they get first strike and that means they can do significant damage in advance. If they're dumb, whelp... Their fault, and they'll live. Probably.
Note that Immunity to Normal Weapons will hurt like hell here. You might want to consider using just the dig team at 6 Shedim.
2: Give serious consideration to halving the Shedim their Edge. Seriously. SRM04-08 admitted Auslander is too tough by halving his Edge. Since SR5 has halved Spirit Edge, it seems no more than fair to apply the same to Shedim. It's bad enough that each Shedim has their own Edge Pool, adding 6 Edge per Shedim to the mix makes it a disaster and results in really high Push-The-Limit results.
3: Environmental Modifiers. If you declare the light to be Dim and the Fog to be Moderate, that's -3 and -3. The light -3 gets boosted to -6 by Shedim power. Ultrasound lets you ignore the -6 and shifts the fog -3 one level up to -1. Thermographic Vision shifts both up 1 row to -1 and -3, so you face a -3.
Note that the Shedim do NOT have this. So while your own attacks will face -3 from the fog+darkness, the Shedim face a -6 from the fog+darkness. This should be a nice balancing factor in the battle, you'll have a hard time hitting (especially Auslander) but the enemy will have an even worse penalty. Not to mention that the normal Shedim charge into melee, so at that point they take a -3 vs ranged attacks.
This -6 (or -3 for Thermographic Vision) also applies to Spellcasting, so Auslander won't be able to score a lot of damage.
4: Overcasting. Auslander should NEVER overcast. He knows full well his Regeneration won't restore Drain damage, so overcasting Toxic Wave is a really bad choice for him. If he goes unconscious while only 1 person remains standing, he dies. So he wouldn't do this.
5: John. If you only have 4 players and they have a hard time in the first battle, consider letting John not get knocked out. If he melees Auslander, that gives the ranged attackers a better chance to hit the doc.
6: Make sure the players remember to play smart. Get them paranoid. Make sure they take precautions, use defensive tricks. They can let a Spirit, summoned before entering the background count, use Concealment on them, or hide between the trees even after the first battle is over, paranoid as one might be that more might be coming. At that point, Auslander might not notice them and they got a shot at doing a LOT of damage even if both sides Edge the roll.
Auslander has 8 Magic, so his Immunity to Normal Weapons is massive. Against an APDS-loaded Ares Alpha he rolls 8+16-6=18 dice and gets (16-6)/2=5 autohits, so on average he knocks off 11 damage. So 1 net hit would translate to perhaps 1 damage. If you use a Remington 950, we're talking 16 dice + 4 autohits for an average reduction of 9.33 vs 12+NH damage, so he'll take a few points. A snipershot, on the other hand, will easily knock off half his health even if he edges and so does the attacker.