Well I will take a shot at this I guess
Firstly I will start with the one that makes the magic happens:
Eevee is quite a cool Pokemon, especially if you have a little cup battle with someone for thanks the the ability in Adaptability it's STAB normal type moves hit like no other. As for it's Nature I recommend one that either raises it's speed or attack but doesn't lower any. The Jolly Nature is often considered as it's best nature as it will be fast enough to perform a notable sweep that once started is pretty hard to stop. I recommend Jolly Nature because it's the only nature that will boost speed and not touch it's attack or defense typing. The raise in speed will make it just fast enough to outspeed many Little Cup Pokemon. Adamant is also a nice nature and works pretty much like Jolly just with favor in attack. So if you don't mind having to risk the chance of having more chance in being outpaced, then go for Adamant. But if you want to be able to hit a hard (Not as hard with Adamant) and be fast the Jolly is the Nature to go with
Hasty/Naive, Lonely are also good natures to run on Eevee but if you are not going to use a mixed set on Eevee then Jolly and Adamant or the way to go
In overall stats Umbreon seems to the bulkier compared to all the Eeveelutions and in fact, it is very bulky but thanks to it's HP and wonderful abilities, Vaporeon will notably survive much longer then Umbreon should it be in rain. Anyhow, Vaporeon has a higher base special defense then defense stat, for this reason investing in it's defense would be way more handier as it will take special attacks relatively good anyways thanks to it's good special defense. To do this it is recommended to go with the Bold Nature on Vaporeon if you are planning to go with Vaporeon the tank/wall. A physically defensive Vaporeon is very annoying as it is the only Pokemon with a base 60 defense that can take a choice Banded Outrage from Black-Kyurem who has a blistering base attack stat of 170.
Anyhow if you want to go for the rather rare offensive Vaporeon who is in fact very deadly Modest is the way to success as it will raise it's special attack and not lower any of it's vital stats. With a raise in it's already high special attack it will be able to nearly OHKO-2HKO everything that comes it's way barring a few grass type Pokemon.
Jolteon's incredible speed enables be one of the fastest Pokemon available. Thanks to it's base 130 speed an nice base 110 special attack stat, investing in more speed is always fun as there are enough items that can help you boost it's special attack stat like the Choice Specs,/Life Orb, For this reason I recommend running a Timid Natured Jolteon because with this nature, there is no unboosted Pokemon in the entire OU tier barring (Ninjask who can be used in OU). There is little use in boosting it's defensive presence for though it has a nice base 95 special defense, it will be hit with a physical move almost 98% of the time and unlike Vaporeon that has HP to boost it's bulk to extreme levels, Jolteon has a low base HP so for this reason running he Timid nature will seem to be your best bet. With this you can easily keep scouting until a Pokemon has died, though if a Pokemon resists Volt Switch you can always hit ridiculously hard with a coverage move such as Signal beam.
Flareon is a hard one. It has formidable stats for a fire type Pokemon but it's drawback is that it has no powerful STAB move for it's highest stat, attack making it rely on weak physical type moves such as Flame Charge and Fire Fang. Howeverr it was also granted a very high special defense stat and it's special attack is certainly not bad so for this reason I will suggest 2 natures that I would say are good and useful and give their best points so that you can chose the one that is most suited for you
Adamant seems like the most logic nature for it seeing as it has a base 130 attack stat but when you look at it's ridiculously shallow movepool. However with the release of Black and White 2 it has been graced with some relatively good Move tutor moves once more. Though you there is only like one effective physical competitive set for it, it can be worth trying out it's physical set where Adamant plays a huge role in it as it will enable Flareon to be quite the offensive presence.
I personally think that a Calm Natured Flareon is the best Flareon mainly because with some investments in it's already high special defense Flareon can be an incredibly hard Pokemon to take down and it's movepool seems to compliment it a lot. With the calm nature it is even capable of absorbing a few water type attacks without the need of sun, though sun would make it quite a special wall. So if you like to stall out your opponents Calm is the way to go though it must be stated that it is in this aspect a little outclassed by Umbreon this is pretty much one of the most effective natures you could run on Flareon
Continued below due to the character limit. I am so sorry :/