What is the Biblical basis for the concept that demons have an odor?

Is there any biblical scripture that explicitly or implicitly suggests that demons have any odour?

Unfortunately there is next to nothing on this subject matter according to the Sacred Scriptures. The Bible does not explain absolutely everything, so sometimes, man has to think outside the box so to speak!

The Book of Tobit is a canonical Scripture Source in both the Orthodox and Catholic Churches, thus the vast majority of Christian denominations. There is an interesting story in relating to this subject matter in the opposite sense.

Upon arriving in Media, Raphael tells Tobias of the beautiful Sarah, whom Tobias has the right to marry because he is her cousin and closest relative. The angel instructs the young man to burn the fish's liver and heart to drive away the demon when he attacks on the wedding night. The two marry, and the fumes of the burning organs drive the demon to Upper Egypt, where Raphael follows and binds him. Sarah's father had been digging a grave to secretly bury Tobias under the assumption that he would be killed. Surprised to find his son-in-law alive and well, he orders a double-length wedding feast and has the grave secretly filled. Since the feast prevents him from leaving, Tobias sends Raphael to recover his father's money.

Here is how the Book of Tobit puts the scene:

18. But thou when thou shalt take her, go into the chamber, and for three days keep thyself continent from her, and give thyself to nothing else but to prayers with her.

19. And on that night lay the liver of the fish on the fire, and the devil shall be driven away.

20. But the second night thou shalt be admitted into the society of the holy Patriarchs.

21. And the third night thou shalt obtain a blessing that sound children may be born of you.

22. And when the third night is past, thou shalt take the virgin with the fear of the Lord, moved rather for love of children than for lust, that in the seed of Abraham thou mayst obtain a blessing in children. - Tobit 6:18-22

Some Catholic exorcists use this as a queue to employ ”blessed incense” in houses possessed by demons.

Strange that incorporeal beings such as demons do not like the smell of holy incense. Devils are not physical beings.

Sacred Scripture, when speaking of demons, always locates them in one of two places: in hell (that is to say, in “that which is below”) or in the air. To say that they are in the air is a way of saying that they are everywhere, that they move about with complete freedom. St. Paul repeats this again when he calls the devil “the prince of the power of the air” (Ephesians 2:2).

2 in which you used to live when you followed the ways of this world and of the ruler of the kingdom of the air, the spirit who is now at work in those who are disobedient. - Ephessians 2:2

Now that the demon are located within man’s atmosphere and being incorporeal entities, it is no wonder that Satan and his Legions are master manipulators of the atmospheric conditions that surround man.

Thus there may be no true biblical scripture source that explicitly or implicitly suggests that demons have any odour, but they know how to set the stage, so to speak, to let people know they are there. It should be noted that this is not a universal demonic phenomenon. They know all too well how mess with man’s reasoning ability.

Many exorcists (regardless of denomination) claim that they can occasionally smell the stench of evil, especially during an exorcism itself.

But the beast was captured, and with it the false prophet who had performed the signs on its behalf. With these signs he had deluded those who had received the mark of the beast and worshiped its image. The two of them were thrown alive into the fiery lake of burning sulphur. - Revelation 19:20

The demon likes to manipulate man‘s atmosphere in order to scare him into submission. He definitely does not what an exorcist and his support team to succeed, so he does what he can to enjoy his morbid freedom for a little longer.

The demon can not do true miracles, but he can manipulate the forces within the air to make it smell like hell, his real dwelling place!

Exorcisms are not for the weak hearted or the weak stomached.

In the bible, KJV, Paul uses both in Ephesians 5:2

And walk in love, as Christ also hath loved us, and hath given himself for us an offering and a sacrifice to God for a sweetsmelling savour.

and Philipians 4:18

But I have all, and abound: I am full, having received of Epaphroditus the things which were sent from you, an odour of a sweet smell, a sacrifice acceptable, wellpleasing to God.

From this we can extract that good deeds produce a good smell.

Furthermore, by not having its sins washed (Revelation 1:5) (reference to cleaning; it might be possible to wash something bad as well, but it's Jesus we're talking about here, if He washes then it gets perfectly washed), the devil is a «corrupt tree» (Matthew 7:18) and so «cannot bring forth good fruit». Therefore, it's not possible for a devil to have a sweet-smelling aroma / smell good.

Assuming one can either smell good or bad, here is the answer you were looking for.

It appears that there is no explicit reference in the bible to point to anything that suggests that demons have any odor.

However, I really wanted to make sense of this (strange for me) phenomenon, so I put some thought into how to understand this.

How do you detect if something has an odor?

You smell it... stating the obvious.

How do you smell something (like coffee)?

With your nose... again stating the obvious

So, how do you smell things in the spiritual realm like demons?

With a spiritual nose or some equivalent.

Spiritual senses

The only spiritual sense that is dominantly shown in the bible is spiritual sight.

2 Kings 6:14-17 (KJV)

Therefore sent he thither horses, and chariots, and a great host: and they came by night, and compassed the city about.

And when the servant of the man of God was risen early, and gone forth, behold, an host compassed the city both with horses and chariots. And his servant said unto him, Alas, my master! how shall we do?

And he answered, Fear not: for they that be with us are more than they that be with them.

And Elisha prayed, and said, Lord, I pray thee, open his eyes, that he may see. And the Lord opened the eyes of the young man; and he saw: and, behold, the mountain was full of horses and chariots of fire round about Elisha.

Taking 2 Corinthians 4:18 (KJV) literally:

While we look not at the things which are seen, but at the things which are not seen: for the things which are seen are temporal; but the things which are not seen are eternal.

It appears from these passages that the ability to see spiritual beings is supported explicitly (for those whom God has given the ability). We can call this spiritual sight.

From spiritual eyes (sight) I would guess that it's not such a far reach to claim that other spiritual senses can exist like

• spiritual ears (hear)
• spiritual nose (smell)
• spiritual mouth (taste)

This makes user19940's answer more complete; if something is "unclean" you can typically smell it (the way I check whether my clothes are clean :P); and if you can smell the spiritual realm then you could be able to smell spiritual beings like unclean spirits like demons (again if God gives you the ability).

This is a bit of a (weird) stretch answer I know, but I hope you found it at least as an interesting view point.