Invisiblity from these powers does not end when you make an opportunity attack.
From Heroes of Shadow, p25:
Effect: You become invisible until the start of your next turn, and you teleport up to your speed.
Nothing in the power says you become visible if you attack.
From the Rules Compendium, p221:
* It can't be seen by normal forms of vision.
* It has total concealment against any enemy that can't see it.
* It has combat advantage against any enemy that can't see it (but it still has to be able to see the enemy).
* It doesn't provoke opportunity attacks from enemies that can't see it.
Nothing in the rules for invisibility says it ends when you attack.
Since invisibility in general doesn't automatically end when you attack, and the power doesn't say that it ends when you attack, it does not end when you attack.
Not having these powers end on an attack is fairly reasonable, since they're reaction powers whose benefit ends at the start of your next turn; you can't use them to become invisible to make normal attacks on your turn. Opportunity attacks and granted attacks (from warlords, etc.) are the only attacks you'll be able to make while invisible thanks to these powers, and those just aren't strong enough to be a real balance issue. Furthermore, there's no way to guarantee that you'll be able to make an opportunity attack during the invisibility period.
The Shadow keyword these powers have is a power source keyword. Just like rangers, rogues, warlords, and fighters have the Martial keyword on all their powers because they are martial classes, and sorcerers, warlocks, wizards, and swordmages have the Arcane keyword on all their powers because they are arcane classes, the assassin has the Shadow keyword on its powers because it is a shadow class. In fact, it is the only shadow class; WotC originally intended to add ki & shadow to the list of power sources, but they couldn't come up with enough classes to flesh them out. Monks were made psychic instead of ki, and assassins got left as the only class of the wildly under-supported shadow power source.
The Teleportation keyword is present because these powers also allow you to teleport. This does not indicate that their invisibility is teleportation-based. There are powers that actually send combatants to other planes for brief periods of time, and they universally remove the target from play for their duration, rather than making them invisible. Invisibility means "present but not visible", as opposed to "temporarily not present".