It works like this.
First theres "IVs" each pokemon has a random value from 0 - 31 as their default "number" in each stat. So HP, ATK, SpATK, SpDF, DEF, SPD each have an invisible number (I say invisible because you cannot see it.) that represents how many IVs the pokemon you own has in that stat. Now these IVs (individual values) basically boost the over all "points" in the pokemon's base stats.
You know how when you get your level five charmander or what have you and it already has stats even though you haven't trained it yet?
That's partially because of IVs and how they boost your base stat. That's why sometimes you'll get a starter and it will have like 12HP instead of 11. Because it's IV stat is higher.
Let's say you have an awesome pidgey. It has 31 in it's speed stat but only 5 in it's attack stat.
There is nothing you can do to change pidgey's IVs higher. Ever. That's just how this pidgey was born. Think of it as pokemon DNA.
Now EVs work like this. Each pokemon you beat gives you a certain amount of EVs.
EVs are kind of like a weird version of EXP. Hmm the best way to explain is it the more EVs you have in a certain stat the stronger it gets.
You can only have 255 in each stat, and a totally of 500 EVs per pokemon. Most people usually just choose two stats to train so they can get the most out of EVs.
Now think of EVs as points every 4 EV points your pokemon gains +1 to what ever stat those EV points are going towards.
So lets say you beat four zubats. A Zubat gives 1 EV point per zubat you beat. So you'd need to beat 4 zubats in order to raise your speed stat by 1+ point.
Now the reason items come into play is for two reason. One when breeding you can actually pass down an IV stat from the parent pokemon to the child pokemon by having the parent hold an item during breeding. So let's say you have a really awesome Pidgey this pidgey has 31 IVs in speed. If it's holding a Power Anklet it will pass down it's speed stat to it's child. Much how you have a 50% chance of the female pokemon passing down it's nature when holding an ever stone. EVs however don't pass down. Since they're "Effort Values".
The second reason they are useful is they make EV training much faster.
If you're Pidgey is holding a Power Anklet it will get +4 EVs ontop of the default EVs your pokemon gets from beating that zubat or what ever pokemon you're fighting.
So if you beat a zubat while your pokemon is holding a Power Anklet you'll end up getting +5 Evs instead of just one in speed.
Here's a run down of each item:
Power Anklet + 4 speed
Power Band + 4 SpDEF
Power Lens + 4 to SpATK
Power Belt + 4 to DEF
Power Bracer + 4 to ATK
Power Weight + 4 to HP
Macho braces are a bit weird. Doubles any effort values the Pokémon holding it gets.
So if you fight a Zubat, you'll get 2+ Evs in speed instead of one.
Or if you fight a Geodude, you'll get 2+ Evs in defense instead of one.
That's why most people prefer the Power items over Macho brace.
Is because even though those items are limited to only giving out EVs in one certain stat it's much faster.
The only real draw back to these items is while the items are equipped your speed is cut in battle.
That's why most the time when you EV train you go after little derpy weak pokemon that are easy to find.
LEVEL DOES NOT MATTER WHEN IT COMES TO EVS. C: So if you kill a lvl 3 Pikachu vs a lvl 40 Pikachu you'll still get the same amount of EVS.
Just you get more EXP from higher level pokemon.
EXP is what makes you level and raises your pokemon's base stat. C:
EVs are more like "bonus" points you get for beating a pokemon.
Remember how as a kid some people would like feed their starter a billion rare candies until it hit like level 100 but for some reason it was kind of weak?
That's because their pokemon didn't have any EVs!
There is also a thing called Poke'rus. It makes it so all EVs received double. This also works together with the power items.
So let's say you have Poke'Rus you're wearing a Power Anklet and you just fought a zubat.
The Zubat gives +1 EV usually right?
Well with the Power Anklet giving it +4 it makes +5.
When you couple that with Poke'rus. That makes it +10 Evs all together.
Which makes things much faster. Trust me I've killed 255 patrats when I was training my lillipup in black.
Never would Ev train again with out at least a power item.
Now to answer your question about "If two pidgey's have the same amount of EVs in the same stat would they be exactly the same?"
Possibly if they had the same IV as each other, in the same stat, along with the same Evs.
If they don't who ever has the higher IV + EVs will be over all higher in said stat vs the other one.
And "stronger" over all.
You also have to take in account natures. Natures effect the growth rate of your base stats.
When it comes down to it natures boost at stat 10% and drop another stat 10%
Any "nature" that is considered a "neutral nature" just means it boosts and lowers the same stat so it cancels it's self out.
Let's say you have a haunter. Haunters have high special attack but really crumby ATK stats not to mention most of their attacks favor SpATKs.
Now we're going to say you want that haunter to have an even higher SpATK base stat.
You'd go for a modest nature, because this nature boosts Special Attack by 10% and Drops Attack by 10%.
And since haunters really have no need for ATK this is a good nature to choose.
You really don't lose anything by having your super low attack stat drop while boosting a stat that's already awesome.
Here's an article that can tell you what each nature does:
Nature - Bulbapedia, the community-driven Pokémon encyclopedia
If you have any more questions lemme know!
Also can't believe I just typed all that.
You don't know how to EV? I can teach you sure! : D