"Then he brought me to the entrance of the north gate of the house of the Lord, and I saw women sitting there, mourning the god Tammuz. He said to me, 'Do you see this, son of man? You will see things that are even more detestable than this.'" NIV translation
Tammuz was the Babylonian god of spring vegetation and supposed died in the fall only to be resurrected in the spring. These women were the nature worshippers of the time and worshipped the creation instead of the Creator. Today, there are the same type of people that praise the creation while denying the hand of the Creator.
"He then brought me into the inner court of the house of the Lord, and there at the entrance to the temple, between the portico and the altar, were about twenty-five men. With their backs toward the temple of the Lord and their faces toward the east, they were bowing down to the sun in the east." NIV translation
The lowest was when they drew near the entrance to the temple and saw men worshiping the rising sun. They had their back to the temple and this was like a slap in the face to God. The equivalent today would be those that do all of the astrology stuff.
"He said to me, 'Have you seen this, son of man? Is it a trivial matter for the people of Judah to do the detestable things they are doing here? Must they also fill the land with violence and continually arouse my anger? Look at them putting the branch to their nose! Therefore I will deal with them in anger; I will not look on them with pity or spare them. Although they shout in my ears, I will not listen to them.'" NIV translation
The sins of the people did not even bother them as they would take part in their idolatry and then attend the temple worship.Putting the branch to their nose was a ceremonial gesture of honoring idols. This was also a reminder that God's people had become a stench to Him. Israel was supposed to be a blessing and a light to the world but now they has sunk even lower than some of the nations around them.