How many stats do they give to the holder and nearby allies? When are they cost effective items?
What if two people have the items, do they stack?
Accurate as of May 2013
Aegis of the Legion is a very cost-effective item, and it now upgrades into Runic Bulwark, which is slightly less cost-effective, but provides more statistics. For just the item owner, with the aura hitting no allies, Aegis is 107.32% gold efficient, and Bulwark is 96.56% gold efficient
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Below is the math, in terms of gold efficiency. I've used the cheapest items available for each statistic to calculate the equivalent gold value of the final item. Obviously if you're comparing against more expensive (and usually more efficient) items, the gold efficiency of the Aegis and Bulwark will fall.
100% gold efficiency means the item is granting as many stat points as if you had spent the same gold on the raw stat items; A higher gold efficiency means you're getting more stat points.
As for the stacking portion of your question, its best handled in a separate question. The short version: If you own the item, you can have double auras, no more; everybody else gets a single aura.
36 gold per 1 health regen
20 gold per 1 armor
20 gold per 1 magic resistance
2.63889 gold per 1 health
Item
250 health, 20 armor, 20 magic resistance
250 * 2.63889 + 20 * 20 + 20 * 20 = 660 + 400 + 400 = 1460g worth of stats
Aura
10 armor, 15 magic resistance, 10 health regen
10*20 + 15*20 + 10*36 = 200 + 300 + 360 = 860g worth of stats
Now, if the aura hits 1-5 champions:
1460g + 860g * 1 = 2320g worth of stats for 1 champion, 107.32% efficient
1460g + 860g * 2 = 3180g worth of stats for 2 champions, 147.91% efficient
1460g + 860g * 3 = 4040g worth of stats for 3 champions, 187.91% efficient
1460g + 860g * 4 = 4900g worth of stats for 4 champions, 227.91% efficient
1460g + 860g * 5 = 5760g worth of stats for 5 champions, 267.91% efficient
The item's total cost is 2150g, so the item is gold efficient for just the item owner.
Item
300 health, 20 armor, 20 magic resistance
300 * 2.63889 + 20 * 20 + 30 * 20 = 792 + 400 + 600 = 1792g worth of stats
Aura
10 armor, 25 magic resistance, 10 health regen
10*20 + 25*20 + 10*36 = 200 + 500 + 360 = 1060g worth of stats
Now, if the aura hits 1-5 champions:
1460g + 860g * 1 = 2852g worth of stats for 1 champion, 96.56% efficient
1460g + 860g * 2 = 3912g worth of stats for 2 champions, 133.73% efficient
1460g + 860g * 3 = 4972g worth of stats for 3 champions, 170.90% efficient
1460g + 860g * 4 = 6032g worth of stats for 4 champions, 208.06% efficient
1460g + 860g * 5 = 7092g worth of stats for 5 champions, 245.23% efficient
The item's total cost is 2950g, so the item is 96.56% gold efficient for just the item owner, and is fully gold efficient if the aura is on at least one ally champion.
Aegis is 1925g. Provides 270 hp, 30 armor, 39 mr, 8 ad to the buyer and 12 armor, 15 mr, 8 ad to nearby teammates. Using stat per gold values found here, it's worth 2191.8g for total stats just for the buyer. For every person next to you, it provides 756.3g worth of stats for them, making the item potentially worth 5217g in stats for the team.
Like all unique aura buffs, it stacks only between the 2 people that have it (prime example is how so many people buy will of the ancients on two ap carries. They each get double aura buff, while the rest of the team only gets one buff).
It is one of, if not THE most cost effective item in the game as far as "team wide" benefiting items. The aura gives every stat you want on a team that needs to be defending, and becomes even more beneficial if your team is behind or losing in any way.
Many times a enemy team that is ahead can be actually beaten by a team with Aegis and decent resistances of their own when defending near their base as they can simply out-last the other team.
As far as the aura goes - the general RULE of aura items in LoL is that they are "unique" in as much as you can only be affected by the same aura one extra time in addition to the aura that you are also giving out. This is why there are "double WOTA" builds where both top and middle lane go AP carrys, both build WOTA and give each other double buff whenever near each other.
For further clarification "An exception to the unique aura rule is in the event that multiple champions are carrying an item with the same beneficial aura effect, each of those two champions will receive two instances of the aura buff: one from the item they are carrying, and a second from the aura of their ally. If a champions is near both of the champions with the same aura item, it will only receive one instance of the aura. No champion can ever receive more than two instances of a unique benevolent aura, regardless of how many nearby allies are providing the buff." Source - http://leagueoflegends.wikia.com/wiki/Aura