Why can demons access a body without permission while Angels have to be invited in? Also, why when some are killed there's just a bright light and other times a cloud leaves the body?
As Cherubel said the bright light appears when a demon is killed. Black smoke is an incorporeal form of a demon.
Demons usually do not have bodies of their own, except in the case of Acheri demons, who can "manifest" as human children. Other demons appear as black smoke in their incorporeal form. Their presence may leave traces of sulfur. They manifest by possessing humans, alive or recently deceased, via demonic possession. - Supernatural Wiki
However when Sam killed Famine and the demons inside him there was no bright light. The scene
It's stated that the angels need invitation to a host body. It's done a few times in season 5. Lucifer, who is an angel, after being released from the cage seeks out a vessel. he finds out Nick, he causes him to hallucinate and convinces him to agree to being a vessel. Later in the season he cannot force Sam into being his true vessel and has to wait for Sam to say yes.
I cannot recall any explanation in the series, but it stands to reason that demons being Lucifer's creation are an act of defiance to God. And if we assume that God's greatest gift to humanity is free will, then giving demons the ability to suppress it seems logical.