Vampires, dragons, werewolves and mermaids all have something in common. That is that they do not exist, or at the very least they do not exist on the physical plane. Some people believe in psi vamps but i will neither confirm nor deny their existence. As for angels and demons i dont think of them as existing in the christian sense which involves horns and halos, but instead in the sense of the greek word daemon which could be any entity of a nature between gods and humans. Please note that people claiming to be such are being less than truthful.
Most mythological creatures and beings, in my opinion, were seen by clairvoyant individuals, through OBE, trance, astral travel, etc and then people formed myth around them. They are spiritual beings, mostly nature spirits. Look at it...a woman with a fish tail, a man with wings, a goat or reptilian like man....does this not scream elements? Fish=water, bird=air, goat/reptile = earth. Spirits can shapeshift freely as they have no physical body to confine them.
Then spirits were categorized by fitting them into special criterias when in reality spiritual beings are all very different. Wings became a sign of divinity, but then why do pixies have them too? So it's related to air, but not all "angels" have wings nor are they all "air" related. So then how can we classify all winged humans as angels? To some winged humans are fae.
The fact is, angels and demons were all "nature spirits" before ever being classified and deamed holy vs evil or even divine or godlike. Holy and evil is a man made physical world term and does not apply to the spiritual world. Wings can be either air, a sign of hierarchy, or be the way the individual spirit wishes to look! Just like some birds have wings and never fly (IE: the ostrich and penguins) looks can be deceiving.
Bottom line is, they do exist but not necessarily the way they are described. And they can be seen in the physical world, but that doesn't mean they ARE physical.