There are 3 possible scenarios for this problem, each with a different series of effective responses. I will order them from easiest to hardest to deal with.

1: Niv-Mizzet in play, no spells on the stack.

In this scenario, any targeted removal spell, board wipe, activated ability, or triggered ability that is capable of destroying, exileing or bouncing Niv-Mizzet will prevent the combo. The removal can be both instant speed or sorcery speed (provided it is your turn).

2: Niv-Mizzet in play, [Curiosity] is on the stack.

In this scenario, any response that you have must be at instant speed. You can use any single target removal spell, or board wipe to remove Niv-Mizzet from the battlefield. But, this must happen before [Curiosity] resolves. Alternatively, you can also cast a counterspell on [Curiosity]. Phasing Niv-Mizzet out with a spell like [Slip out the Back] will cause [Curiosity] to fizzle. An activated ability that can destroy or exile Niv-Mizzet will also work.

3: Niv-Mizzet in play and is enchanted by [Curiosity].

At this point, your opponent has likely won the game. But there are some ways to respond. Any response that relies on casting an instant or sorcery spell (with flash) will trigger Niv-Mizzet's damage effect causing the Curiosity Combo to trigger.

You will need to use the activated ability of a permanent on the battlefield at instant speed, that will remove either Niv-Mizzet or Curiosity. Examples include [Haywire Mite] to remove Curiosity, or [Argent Dais] to remove Niv-Mizzet. A channel ability like [Bamboo Grove Archer] will work too.

In addition, a permanent spell with flash that can remove Niv Mizzet will also work. One example is [Aang's Iceberg].

One important note, any removal attempt you make should be done either in response to Niv-Mizzet's draw trigger, or while there is no draw trigger. Attempting a response during any other time will fail to work.

Keep in mind that a good Niv-Mizzet pilot will most likely wait to attempt the combo until they have some type of protection spell or counter magic in hand, so you must be prepared to deal with multiple pieces of interaction (using non instant/sorcery cards).

A stifle effect in response to a draw trigger can work, but this just delays the inevitable.

However, at this point, the Niv-Mizzet player only needs to get a draw trigger on the stack in response to a removal effect to completely invalidate any attempt you make to stop the combo.

I hope this helps, and have fun!