The strangest funerary custom to come will be the memorializing of the dead online. It has already started with little monuments and the like left in online games that have persistent worlds, such as Eve and Second Life. But in the future there will be gamers who donate money to online spaces to build structures named after them, which will remain long into the future, as we do with earthly monuments now. There will be online graveyards, where the bereaved can visit a virtual memorial for the dead.
There will even be social media memorials, where dead people's profiles live on, interacting with the world in ways that are preprogrammed, such as showing old photos or republishing old posts on meaningful days, so that the friends and loved ones of the dead can revisit them. This will be especially meaningful for many who felt close to the person who passed, but only knew them in the digital world, never having met them in life.