What would you call a person who is self-righteous, brags about her/his moral values and is imposing when it comes to her/his ideas?

I want to describe, in a phrase, a number of traits in a person.

I'm looking to describe a self-righteous, pious person who cannot stop bragging about her/his moral values while trying to impose her/his ideas on to those with whom she/he talks frequently. One may imagine such a person to also have related characteristics such as being highly assuming and judgmental. The main things I want to describe are the person's bragging and imposing nature. I thought of 'self-righteous bragger' but I don't think it covers it all, especially, the imposing part (or can it be said that a self-righteous person is also imposing?). 'Self-righteous imposing bragger' also doesn't sound right. Can you suggest better ways to describe all these traits in another phrase?

Sanctimonious will do.

Per Macmillan:

sanctimonious (adj., showing disapproval): used for describing someone who tries to show that they have better moral or religious principles than other people

"I was aware even as I spoke how sanctimonious I sounded."

Synonyms and related words describing arrogant and over-confident people or behaviour: arrogant, proud, conceited...

_{Fun story: I was once playing Pictionary, teamed up with my mom. It was her turn to draw, and she started sketching a bishop sneering down his nose from a pulpit on high. The answer was sanctimonious. We crushed the other team.}

holier-than-thou

• marked by an air of superior piety or morality
  • having or showing the annoying attitude of people who believe that they are morally better than other people. (MW)
    • excessively or hypocritically pious (Vocabulary.com)

pharisaic

• Someone who exaggerates how morally upright or pious he/she can be called pharisaic.
  • Another way to say it is "holier-than-thou." (vocabulary.com)

Pharisaic people tend to talk a lot about how devout and religious they are, but their actions don't quite measure up to their words.

An entitled or pontificating individual would share the qualities you've described.

"Entitled" (Google Query):

believing oneself to be inherently deserving of privileges or special treatment.

"Pontificate" (Google Query):

express one's opinions in a way considered annoyingly pompous and dogmatic

I think self-righteous and braggart (not bragger) are indeed the correct terms for what you're describing. The word you are missing is overbearing, which Google currently defines as unpleasantly or arrogantly domineering.

So your complete phrase would be:

An overbearing, self-righteous braggart.