Let's begin with the Orb Effects Priority Table (Click to enlarge)

This table simply says it all (If you are confused why there's a Cold Attack : Ranged for Melee heroes, just bear with me, I will explain why later on).
As you can see, LifeSteal has highest priority than all other item orb effects. So if you have a Helm Of Dominator (Life Steal) and a Sange & Yasha (Maim), you will get only LifeSteal. Maim will not happen due to its lower priority than LifeSteal (which led to confusion few days back, just try it, it's true).

Nevertheless, the story gets little complicated when it comes to Eye of Skadi. Eye of Skadi for melee heroes is an orb effect, and it goes like the rest of the orb effects. However, Eye of Skadi for Ranged Heroes is NOT AN ORB EFFECT. Yes, you heard me right. Its NOT. Instead, it's a debuff placed on attack, so it stacks with some other orb effects, which will not place a debuff on the attack.
For history lovers and tech maniacs, DotA was programmed in such a way that only a single debuff could be placed on an attack, so multiple debuffs cannot take place with a single attack.
So as you can see, if you are a ranged hero and you have an EoS with Satanic, both Life Steal and Cold Attack will take place, as Life Steal is not a debuff. If the hero has a Maelstorm, the debuff will be placed only when Chain Lightning occurs, so when Chain Lightning occurs, it will override the Cold Attack. However, in other attacks, Cold Attack will take place.
Things get even more interesting when it comes to Feedback with a ranged EoS. As the table says, if the target has mana, Feedback will take place, and if the target has no mana, cold attack will take place. So this means, if you hit a melee creep, cold attack will occur, but if you hit a ranged creep or a hero, feedback will occur. Now for those who think that I made a mistake by saying "hero", here's my explanation. As we all know, heroes have a HP regen and a Mana regen. With the heroe's mana regen, the chances of having a hero with zero Mana is so low that it will never happen. Before you make the next attack, 99% of the time, hero will regain at least a single mana point. So in practice, it will not work.
Finally, here's a word about having Cold Attack : Ranged on Melee heroes and Cold Attack : Melee on ranged heroes. If you haven't figured it out yet, think about heroes like Terrorblade or Troll Warlord. Those heroes can switch between melee and ranged modes. So it matters to such heroes. However, take notice that the "type" of Cold Attack is not determined by the current mode of the hero. It depends on the mode of the hero which was when he picked up EoS. For example, if a Terrorblade picks up EoS in Melee mode, it's a Cold Attack : Melee. Even if he transforms to ranged afterwards, it will still be a Melee Cold Attack, vice versa.
This took me about 30 minutes to write down. But it took so long to find out these stuff. So I believe my effort would help out DotA maniacs out there to play a better game.
GG.
Update (03-June-2008):
Hero Orb Effect Skills Table (Click to enlarge)

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