The ideas below are just that - ideas. Aside from the first one, I wouldn't consider any of them essential for an undead elder brain, but they could add a nice touch and flexibility to it.

Not strictly stats, but remove the need for food, drink, air and sleep.

Undead often have this trait. Feel free to not remove the need for food/drink if you think that's thematically more suitable for an elder brain, or replace its need for brains with a need to sacrifice souls to Orcus. Either way, get rid of any requirement for air and sleep, if the elder brain needs those in the first place. The rules don't state anything like that as far as I can tell, but I think it's justifiable to rule that an elder brain doesn't need to breathe. The same goes for sleeping.

Add "undead-themed" legendary actions

This could be something like "everyone within X feet of Cyrog takes Y necrotic damage", a targeted attack that turns its victims into undead if it kills them, or an action that turns Z number of corpses into undead. ("Undead" here means zombies, skeletons or ghouls)

For reference, see the Lich's Disrupt Life legendary action:

Disrupt Life (Costs 3 Actions). Each living creature within 20 feet of the lich must make a DC 18 Constitution saving throw against this magic, taking 21 (6d6) necrotic damage on a failed save, or half as much damage on a successful one.

Add some way for the undead elder brain to create undead

This could be done via spellcasting (Innate or regular), via Legendary Actions (see also above), Lair Actions or regular actions such as a Wight's Life Drain.

Looking at Orcus statblock in MToF, I'd also add something similar to Orcus' Master of Undeath feature - i.e. a Gift of Orcus, which allows the elder brain to control undead it created indefinitely.

Add Magic Resistance

The Dracolich template for creating undead dragons lists this feature.

The dracolich has advantage on saving throws against spells and other magical effects.

Challenge Rating

Depending on how which features you add, the CR could change. I recommend you check out the section on Creating Monsters in the DMG, page 273-281.

Looking only at the features you added, we can see the following:

• Elder Brain base stats: CR 14
• +4 CON = +2 HP per hit die = 20 hit dice * 2 = +40HP. HP-wise, the elder brain would usually be CR 10, with this change it would be CR 12.
• Resistance to necrotic, cold and lightning: These are a bunch of resistances against fairly common damage types. Therefore, we apply a 1.25 modifier (see DMG p. 277) to the effective HP (not the real HP, just for comparison), seeing as we'll probably end up in the 11-16 CR range. This leaves us with 250 * 1.25 = 312 HP, which would put us at CR17.
• Immunities to poison and nonmagical physical damage: at the point where you fight beefed-up elder brain, noone in your party should be dealing nonmagical damage anymore (excluding bow-using party members, since magical arrows are kind of hard to come by, depending on the DM). Therefore, I believe we can ignore this immunity, it will more or less only affect summoned creatures and the like that don't deal magical damage. Combined with poison resistance, however, I'd change the 1.25 modifier from the previous point to 1.5, meaning that we're now looking at an effective 375 HP, which equals CR 20 (keep in mind that this is just the HP-based CR, there are other factors).
• Condition immunities: Most effects that cause conditions are neglectable for high-CR creatures with good saves and the Legendary Resistance feature like dragons, or in this case, an elder brain on undeath steroids. Therefore, I wouldn't value this buff too highly, although it's certainly helpful.
• Turn resistance: I would change this to Turn Immunity. Elder brains are pretty much completely immobile, so it can't run away. However, failing this single save would effectively take them out of combat for 1 minute or until you deal damage, meaning that you could wipe out all its servants without being bothered. This would be way too overpowered, therefore I would change it to Turn Immunity. Granted, elder brains have Legendary Resistance, but I think it'd be better (and also more suitable lore-wise) to make them immune. For reference, Demiliches, Revenants and Crawling Claws also have Turn Immunity.

In conclusion, we end up with a challenge rating difference of +5. The CR is calculated as

$$(offensive CR + defensive CR) / 2$$

We didn't add any offensive benefits, and the defensive CR increased by 10, from 10 to 20. We're looking at HP only here - other defense-related factors like AC are the same as before, so whether they lower or raise the defensive CR doesn't matter.
Therefore, the average CR increases by 10 / 2 = 5, meaning that we end up with a CR of 19.

I personally think this is too high, since the resistance- and immunity-based HP modifier table is a bit over the top in my opinion. Notably, if your party is only dealing magical slashing/bludgeoning/piercing or fire damage, they won't notice the resistances and immunities at all.
Ignoring the resistances and immunities, we would be at +2 defensive CR (+1 total) only, hence I'd go with a compromise and increase the CR by 2, to 16. This should, however, differ according to the damage types that your party usually deals.

The answer in this question has a useful link from Wizards of the Coast. This document contains guidelines on converting to 5e, including a "Quick Conversions" section on the last page, with a subsection for Monsters. For third edition monsters, that section includes:

Most statistics in third edition include the creature’s ability scores. Use the following parameters:

• Armor Class can be an average of touch AC and actual AC, or 20 percent lower than in third edition. The upper limit is 22.
• Attack roll modifiers are the appropriate ability score modifier + 3.
• Saving throw DCs are 10 + the appropriate ability score modifier.
• If a creature has to make a check or saving throw, use its ability score modifiers. Grant it a +3 bonus if it should be good at the roll.

Good luck.

It's worth noting that while ability scores in 3e tend to be higher than the 5e equivalents, the quick conversions only grant a +3 proficiency bonus. This will generally keep attacks for high CR creatures near sane levels, though do not be afraid to hard-cap attacks at +12 (the DMG recommended attack bonus for a Challenge 20 monster), at least for non-epic foes.