When you multiclass your spell slots change to match the table (Pg 165 PHB). Those spell slots are shared between all your spell casting classes and can be used in any combination. You would then have all those slots available for Divine Smite.
2 Paladin/3 Sorc/2 Warlock
Gives you 3 spell level for Sorc, and 1 for Half Paladin level. This makes you spell level 4. Giving you 4 first level slots and 3 second level slots. Your paladin levels contribute to your spell slots so therefore you could use any of those for Divine Smite.
You would be able to use the warlock pact slots to cast Sorc spells but as Paladin Levels do not contribute to your pact slots only spell slots they would not be usable for Divine Smite.
Most other spell casting refers to the use of Spell Slots in general and not a class specific spell slot. This case of Paladin Spell Slot leads to the answer above.
Depending on DM interpretation some DM's might rule that Warlock pact slots can be used and others would rule otherwise. If the DM lets you use warlock pact slots then the Divine Smite would be used at the level of the spell slot.