An excerpt from the article on the Meal Offerings and Their Implications by Rabbi Moshe Odess in Maalin Bakodesh, issue #2
The Meal Offering Offered by the Sinner
By the Sliding-Scale Offering it is stated:
(Vayikra / Leviticus 5:11) If he cannot afford the two turtle doves or two common doves, the sacrifice that he must bring for his sin shall consist of 1/10 ephah[i] of wheat meal as a sin offering; since it is a sin offering, he shall not place any oil nor any frankincense on it.
And by the offering offered when a woman is suspected of adultery (Sotah), it is said:
… when he brings her, he must also bring a sacrifice for her consisting of 1/10 ephah of barley meal. He shall not pour oil on it, nor place frankincense on it, since it is a jealousy offering. It is a reminder offering to recall sin (Bamidbar / Numbers 5:15).
The non-giving of oil in these offerings is explained by the Chinuch as follows:
Because the oil hints to an elevated status and greatness, for if you mix it with all liquids it floats above all of them, and it is a very important thing, and the importance of the good oil is well-known, and therefore those in training for kingship or priesthood will be anointed by it; therefore it is not fitting to put from it onto the meal offering of the sinner, who needs to show in himself worry and lowliness on account of the matter of transgression that came to his hand (Sefer HaChinuch, positive commandment 129).
And so the Maharal wrote:
And you will find that there are three properties in the meal offering. One is wheat meal that is clean and pure, and it is parallel to the body that is clean of all waste products that are (naturally) present by it… And upon it, the frankincense which represent the merit of proper actions. And upon it, the oil, which is clean and pure, which represents a pure intellect… and therefore he would put the pure frankincense on the meal offering, for he merits to have good deeds, which comprise a good reputation, all in accordance to how he purifies his body….
And here you will find in the offering offered when a woman is suspected of adultery, that she was inclined to follow after materialistic things, that she did the act of a beast; the Torah said that the meal offering should be of barley, not clean wheat meal, in accordance to what she did, that she was drawn after the materialistic  and therefore it is written ‘He shall not pour oil on it, nor place frankincense on it‘ (Bamidbar / Numbers 5: 15), because she continued after the materialistic and after the beast  therefore the meal offering in this instance lacks these two, etc. (Drush Naeh, page 217).
And so too wrote Rabbi Kook:
The oil is already a suitable matter for spiritual illumination, the substance that illuminates and drives away the darkness, brightens the face, and awakens a state of honor in its anointing, it recalls Divine Inspiration and the esoteric secret of rest and the advent of the Divine in its clear light, this supreme power is already mandated to be revealed in a well rooted fashion, in the natural characteristics of the world of vegetation, of man, and of the nation… 
According to this basis, it is possible to explain the ruling given in Rashi on the verse “from the wheat meal of the offering and from its oil” (Vayikra / Lev. 6:8): “From here we derive, he takes, a kometz[ii] from the more oily section”, as an expression of the more spiritual side of a person, which must be sacrificed – subjugated to the One Most High.
We can, therefore, summarize: the relationship between the wheat meal and the oil symbolizes the degree of penetration of the spirit in the human body, and therefore the sinner does not mix oil in his offering. 
[i] According to Rabbi Kaplan’s translation 1/10 ephah. Around 2 quarts. See Exodus 29:40.
[ii] A pinch of the meal offering filling up the space between the tips of the index, middle, and ring finger pressed together onto the palm of the hand.
 In section 12:3 of the article by Rabbi Moshe Odess, he mentions that the Omer offering also comes from barley and it also symbolizes the materialistic state of the children of Israel when they left Egypt. Nevertheless, since it is not brought on a specific, defined sin, we put in it oil (See Sotah, Chapter 2, Mishna 1), which is not the case for the meal offering brought when a woman is suspected of adultery, that she did the action of a beast.
 It is possible that Rashi had this notion in mind in his commentary to Bamidbar / Number 5:15 “he shall not pour oil upon it”: “that her offering shall not be of superb quality for the oil is called light, and she acted in the dark”, that is to say the darkness of materialism overpowered the light of the intellect.
 Rabbi Avraham Yitzchak HaCohain Kook, Olat Ri’iyah, vol. 1, Jerusalem 5709, page 131
 According to this one should investigate why the Mishna in Menachot 5:3 lumps the 2 loaves of bread brought on Atzeret (Shavuot), that definitely doesn’t come on account of sin, together with the meal offerings that come on account of sin. As stated “the 2 loaves of bread, the meal offering of the sinner, and the meal offering of jealousies, do not receive oil or frankincense”. In chapter 12:4 of the article by Rabbi Odess, the author attempts to explain this exception.