Here's the case scenario:

A berserker called from a Horn of Valhalla attack a Lich with his greataxe action.

Does the Lich suffer damage since he's immute to non magical slashing damage?

Since the berserkers magically called from the horn are "warrior spirits" does the attack they do are "magical"?

Thank you all in advance!

This answer in the SAC is closely related to the question:

Is the damage dealt by a beast from conjure animals considered magical?

The stat block of a conjured creature determines the nature of the creature’s damage, unless the spell says otherwise.

Also, if you follow this advice from the SAC, I'd say neither the berserker nor their attacks are magical:

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Is the breath weapon of a dragon magical?

[...] Determining whether a game feature is magical is straightforward. Ask yourself these questions about the feature:

• Is it a magic item?
• Is it a spell? Or does it let you create the effects of a spell that’s mentioned in its description?
• Is it a spell attack?
• Is it fueled by the use of spell slots?
• Does its description say it’s magical?

Thanks!