When should I buy Sword of the Occult or Mejai's Soulstealer?

I have to say I almost always buy the soulstealer when I'm playing Normal games with friends that have a lower rating than me. It is a really great gameplay experience if you know how to play with such a high risk item.

But for serious competitive play: Don't Buy it!

It's really only good if you are 100% sure that you're gonna snowball this game and it's a huge wast of gold if you die once. For competitive builds replace the item with another Offensive or maybe even defensive one. But if you are platinum or diamond and you're playing normal games with your bronze and silver friends, go ahead and have fun with the item.

An additional thing: The AD Item isn't that useful. Usually you are better off with normal AD items.

In almost all cases, you should not buy this item. You should only even consider buying them when you know you'll be able to maintain at least 5 stacks (7-10 is much better).

As a result of this, in most cases, an AP or AD carry should rarely (never) buy these items (as outlined in @Haidro's answer.)

BUT, there are some supports that can make decent use of Mejais. Supports that can't help but to get assists and have AP scaling can make use of Mejais. These supports are generally Janna, Soraka and sometimes Sona. While the item is less risky on a support, you still have to (on average) get 3 stacks (3 assists or 1 kill and 1 assist) per death. If you're doing poorly in lane, it would be a bad item to acquire.

There is only one case where I would buy Sword of the Occult, and it only really works in lower ELO. That case is using Yi. Once again, due to alpha strike and reset potential, he can get a lot of assists or kills in-between deaths.

Once again, the key is to get 5 stacks and then get an average of 3 or more stacks per death - then at least the item will be 'gold efficient'.

Either way, in practice, I buy one of these two items in less than 1% of my games and never in a competitive game. Although, I do tend to buy it when fooling around versus bots.

I think these are items really gameplay-dependent. You should only buy them if you feel like that is a good idea (and if you know you'll get feed of course).

Champions that are very dependent on snowballing should use these types of items.

For instance, Draven has a hard time if he does not snowball due to being out of reach of the kill. It stalls his passive which prevents you from snowballing. However with SotO in your inventory as him, he will gain 5 damage per assist. Now it might not seem like much, however, when he levels up, or gains the first Dragon buff, or simply buys his next item, missing those kills suddenly isn't as detrimental to his snowball potential.

On the other hand, Mejai's Soulstealer is a must for certain champions with a high late-game curve. Consider the fact that you are purchasing mid-game power, and it naturally transforms into late-game power before you actually get to late game.

That type of power spiking, combined with the knowledge to end the game quickly, will make enemies heads spin.

For instance, a Lich Bane Lux in mid with Mejai's will be the fastest tower pusher in the match if she is proper.