Remember, in Little Cup, all Pokemon are at level FIVE. It's also a very fast-paced sort of environment- walls don't usually do well there.
Considering EVs are distributed as the Pokemon levels up, all 252 in a stat aren't going to be crammed in through four levels of raising. Basically, you're probably investing WAY more in each individual stat than what you need, and could probably stand to invest some in other stats, like defensive stats. For instance, that Murkrow might not have to invest 252 Spd EVs to reach its max potential, and those leftover EVs might boost up Atk or Sp.Atk another point. PokeSav and Shoddy are useful for determining the max number of EVs that will benefit a Pokemon the most.
It looks like a Nasty Plot Croagunk could really do a number to this team. It could probably OHKO Probopass, Azumarill, AND Eevee with Vacuum Wave (easily setting up on Azumarill OR Probopass), Drowzee with Dark Pulse... Murkrow, being Naive, would also take quite a number from Vacuum Wave, considering its frail defenses.
A max Spd Carvanha mixer might have something to say to your team, also, particularly Growlithe and Drowzee.
As for individual sets, the only one that bothers me at all is the Azurill. It has no Spd investment, no Salac, and no real bulk to speak of. You'd have to set up against a sleeping foe or something, and even then, the next Pokemon that comes out is probably gonna kill you. Scarfed Pokemon are very popular in Little Cup. Like Diglett.
Edit:
Now that I look at it, you might want to consider Intimidate on Growlithe, also. Your team doesn't look like it would tempt many Fire attacks, really.
By the way, did some calcs...
Buizel @Lum Berry/Leftovers
-Waterfall
-Aqua Jet/Quick Attack
-Filler
-Filler
Swift Swim, Adamant
236 Atk, 236 Spd, 36 whatever
You've been swept. Buizel with Waterfall and Aqua Jet can both outrun AND OHKO everything on your team. Yeah, Waterfall takes out Nosepass with, like, 500% damage +, minimum. Aqua Jet and Quick Attack can BOTH easily OHKO Murkrow.
This isn't meant to sound rude, or cocky. I'm just showin' you an example of how fast-paced Little Cup can be.
Priority is popular in Little Cup. As such, I would STRONGLY suggest you change that Eevee. It does wonderfully in Little Cup because of its raw power, thanks to Adaptability, but Flail/Reversal sets just don't work in this kind of environment.
Eevee @Focus Sash
-Return/Frustration
-Protect
-Yawn
-Quick Attack
Adaptability, Jolly
236 Atk, 36 Def, 236 Spd
I'd consider something like this. This Eevee plays out a little less predictably, and a little more strategically. You can scout with Protect, and switch in and out based on what attacks they use (keep in mind that Sashed Pokemon are VERY popular in LC). Return, clearly, is your main offensive move, and it's gonna sting somethin' fierce. If you're up against something like that Buizel I put up, since you've got that Sash, you can probably Yawn it and Protect the next turn, like your original plan had been, and hope they're not packing a Lum Berry or Substitute (personally, mine would). Afterwards, you would definitely OHKO with Return, and probably OHKO a less durable Pokemon with Quick Attack before taking a fall.
Scarfed or Sashed Venonat leads could work out well, since they get Compound Eyes Sleep Powder AND Stun Spore. Croagunk would also do your team a WORLD of good, thanks to Dry Skin.
Pretty much, whoever has the faster, stronger priority attack wins. Got an ExtremeSpeed Zigzagoon?