I know that druids/wizards can summon elementals, but can sorcerers summon them without multiclassing?
When Sorcerers get to 17th level, they have access to the Wish spell. This spell can replicate any spell of 8th level or lower, including Conjure Elemental and Conjure Minor Elementals.
Furthermore, they can be given a Ring of Spell Storing which contains one of the Elemental-summoning spells, pre-charged by a Wizard. They will be able to summon the Elemental as if they had cast the spell.
Yes, with magic items
The DMG has the Bowl of commanding water elementals, Brazier of commanding fire elementals, Censer of controlling air elementals, and the Stone of controlling earth elementals.
Each of these items allows you to summon their respective elemental as if you had cast the Conjure Elementals spell.
Of course, one could use Wish or any of the other ways to transfer spells, but these items are a more direct way of replicating that ability without using up spell slots.
No, not inherently, or specific to being a sorcerer.
There are magic items that can allow them to summon elementals, but those could equally well apply to any spellcaster class, and have nothing to do with being sorcerer, per se. Within the powers of the sorcerer class, there is no provision for summoning or controlling elementals, short of using the Wish spell for that at 17th level plus.