From the Necrons 7th Edition tactics. Mephrit Dynasty Relics section
You DEFINITELY can't take multiple of the same Relic, but I'm inclined to believe you can take both the Solar Thermasite and the Nightmare Shroud. They're two separate Relic lists. Playing a Mephrit FOC lets you take any of the RotWiH, and the codex lets you take ONE of the AotA.
Relics are a bit wonky. Some supplements can take both their own relics as well as those of their base codex, some can't. In the case of Mephrit Dynasty, I've seen the ruling that you can take only one relic per character, although you can take it either from Mephrit or base codex (provided your character is from a Mephrit Dynasty formation, of course), but that isn't an official GW FAQ.
"Characters with the Necrons Faction that are part of a Detachment or Formation presented in this book can select an item from the Relics of the War in Heaven list at the points cost shown. Only one of each of the relics may be chosen per army - there is only one of each of these items in the Galaxy."
All that states is that a character can select one, and that there cannot be duplicates, as in two Solar Thermasites.
It doesn't say you can't take Artefacts of the Aeon if you're in a MDD, and it doesn't can't take one if you take a Relic of War.
RAW should read like this:
A Necron character can take one Artefact of the Aeons, and a Necron character can take one Relic of War.
So does that mean I can have a Necron Overlord/Destroyer Lord with a Nightmare Shroud and a Solar Thermasite?