For exorcists: Allen, Kanda, Miranda, and Lenalee are all still alive! Miranda's Innocence reacted to Allen's misplayed song, sending them forward in time thirty years (as of yet the Ark hasn't reappeared, but when he gets cannonmates he'll get sent back for an update). They're all the same age, as they were inside the ark while time moved around them.
Timothy is a general now, and Tiedoll died from old age.
Generals and former branch heads travel together for protection (Cross and Komui, Bak and Klaud, Renee and Timothy, Zokalo travels alone because he's crazy) and are almost constantly on the move. There is an "HQ" it changes places almost constantly, and is more of a place for the science members to gather than anything. Civilians now treat Order members with disgust and fear, considering them heralds of destruction as the Earl, Noah and akuma hunt them down and raze everything in their way. This means the Exorcists have to be extra careful with who they trust, as informants are often greatly rewarded for the head or even location of an Exorcist.
For Noah: There are now two level 5 akuma in existence- their names are Madama (masculine) and Lilith (feminine). They chose the names themselves, and mostly keep to themselves for now, hidden away in the mansion. There are seven levels of akuma evolution, and humanity is proportioned as such that only two akuma can reach the final level, providing they eat all other akuma and destroy every last human. Once the two akuma reach the final level the Earl will sacrifice each Noah, bestowing their "memory" onto them before sacrificing himself. The akuma would be able to reproduce upon reaching level seven, thus creating a new, perfect race of "inheritors of the earth"- or at least, that's how the Earl sees it. Only the 14th and the Earl know explicitly about the literal "sacrificial lamb" part of being a Noah (Bookman, Tyki, Road and Wisely have all fairly guessed), while only Road and the Earl know about the existence of level 5 akuma.