Venomous manticore reads "... Kneel 1 influence to attach it to another character" so if I attach it to a character with 3 strength then later lower that character's strength to 0 and kill it can I move venomous manticore to another character before that character is killed? If I can't move manticore I guess it would be discarded from play just like any other attachment.

In your example the manticore would be discarded. The timing doesn't allow for the player action of kneeling the influence to move the manticore before it would go moribund and leave play