Is there an upper limit to the damage that Eldritch Smite can deal?

Eldritch Smite caps at 6d8 force damage, or 12d8 on a critical hit.

The Eldritch Smite invocation specifically requires a "warlock spell slot", referring to spell slots granted by the Pact Magic feature. According to the multiclassing rules, spell slots from Pact Magic do not combine levels with spell slots from Spellcasting.

Spell Slots. You determine your available spell slots by adding together all your levels in the bard, cleric, druid, sorcerer, and wizard classes, and half your levels (rounded down) in the paladin and ranger classes.

Warlock is not listed among the classes here. It gets its own section:

Pact Magic. If you have both the Spellcasting class feature and the Pact Magic class feature from the warlock class, you can use the spell slots you gain from the Pact Magic feature to cast spells you know or have prepared from classes with the Spellcasting class feature, and you can use the spell slots you gain from the Spellcasting class feature to cast warlock spells you know.

So a Warlock 5 / Sorcerer 15 would have 3rd level spell slots from the warlock's Pact Magic, and 8th level spell slots from the sorcerer's Spellcasting. They can use their sorcerer spell slots to cast warlock spells they know. However, Eldritch Smite does not involve casting a spell, thus the character cannot expend their sorcerer spell slots for Eldritch Smite.

Suppose the character instead had 9+ levels of Warlock, granting access to 5th level warlock spell slots. If they expend a 5th level warlock spell slot using Eldritch Smite, the force damage is 1d8 + 1d8 per spell level, or 6d8 total. And if the triggering attack was a critical hit, then these dice are doubled for 12d8 damage.