Diablo – stay on normal difficulty and continue to level up

There are a few differences that are known and probably more as well:

1. Higher difficulties mean higher tier loot. Jay Wilson stated that over 70% of all of the armor items in the game cannot even be found in Normal difficulty. So as the difficulty raises so do the armor tiers. One can assume 4 per act totaling 16 tiers. Remember, tiers don't necessarily mean better, just different looking.

2. As the difficulty increases, the boss monsters become more powerful. More specifically, in each difficulty, the monsters gain one more special ability. By Inferno, they can have up to 4 special attributes which can make them very difficult to take down.

3. More obviously, the standard enemies will scale with the difficulty. This video says that monsters scale much like they do in diablo 2. They all have set stats which they carry with them as they level. The monsters also have more awareness and abilities as they scale through the difficulties.

4. Also, you progress through the difficulties, you can upgrade your artisans more through items that drop only in higher difficulties. However, as noted by @Kexlox you can also buy the tomes from the AH and upgrade your Artisans early.

Keep in mind while playing that Normal is made to basically be the tutorial and break you into the game. Experienced D2 players will cut through Normal with ease. As you progress, the game does get very difficult, and you'll be wearing your butt on your head once you reach Inferno. Inferno was basically built to murder you. Jay Wilson stated that they took the hardest difficulty that their testers could handle and agreed was fair and they doubled it.

FROM BRYSONIC'S ANSWER -

The difficulty also scales by having additional players affect monster HP. Monster damage used to scale, but no longer does as of patch 1.0.3.

Note: Because of patch 1.04 monster health per additional player now is not effected by difficulty.

Here is a table showing the amount of scaling that occurs based on the number of players in the game:

This table is now technically useless, but I will leave it here as a placeholder.

          Normal          Nightmare          Hell            Inferno
         ===============  ===============  ===============  ===============  
Players    HP    Damage     HP    Damage     HP    Damage     HP    Damage  
   1      100%    100%     100%    100%     100%    100%     100%    100% 
   2      170%    100%     170%    100%     170%    100%     170%    100% 
   3      240%    100%     240%    100%     240%    100%     240%    100%
   4      310%    100%     310%    100%     310%    100%     310%    100%

I had the same problem when I first faced these critters on my Monk. They are the first enemy that caused me to change my skill loadout.

There are Resist Poison items (easily searchable on the AH) that would help you against the insects in particular, and more armor always helps, but I found the right combination of tactics was all I needed to bring them down.

My best advice is to keep moving. The attack moves pretty slow and if you see it coming, it's not too hard to dodge. But as you said, all too often you are distracted by other foes. So here are a few tips and tricks to deal with those pesky flies as a monk.

• Dashing Strike is by far your best ability to deal with the flies. Don't be afraid to use this on the target with a line of projectiles coming straight at you. The dash will go straight through them and you won't take any damage.
• Cyclone Strike followed by a good AoE attack is usually enough to take them out. Don't use a knockback as a followup or you'll just have to start dodging and chasing again. I choose Breath of Heaven with the Circle of Scorn rune.
• Fleet Footed will help you dodge the attacks and catch up to the flies when they move away from you.

This probably goes without saying, but if you are playing multiplayer with a ranged partner, have them focus on the flies while you take out the other opponents.