The bad breath and body smell:

[Md. Siddiqul Alam (Reza)]

The bad breath and body smell:
Jabir b. 'Abdulla h reported the Apostle of Allah (may peace be upon him) saying:  "He who eats of this (offensive) plant, i. e garlic, and sometimes he said: He who eats onion and garlic and leek, should not approach our mosque for the angels are harmed by the same things as the children of Adam.  (Translation of Sahih Muslim, The Book of Prayers (Kitab Al-Salat), Book 004, Number 1147)"

Narrated Jabir bin Abdullah:  "The Prophet said, 'Whoever has eaten garlic or onion, should keep away from us, or should keep away from our mosque and should stay at home.' Ibn Wahb said, 'Once a plate full of cooked vegetables was brought to the Prophet at Badr. Detecting a bad smell from it, he asked about the dish and was informed of the kinds of vegetables in contained. He then said, 'Bring it near,' and so it was brought near to one of his companions who was with him. When the Prophet saw it, he disliked eating it and said (to his companion), 'Eat, for I talk in secret to ones whom you do not talk to.'  (Translation of Sahih Bukhari, Holding Fast to the Qur'an and Sunnah, Volume 9, Book 92, Number 458)"

If a person has a bad breath, then he not only will harm his fellow Muslims, but also the angels as well.  Notice that the first Saying of our beloved Prophet is not just limited to bad breath.  Any type of bad smell that comes out of a person is not accepted.  This could be the smell of bad body sweat, morning breath, etc....   These people are not allowed near the Muslims or the Mosques.

Narrated Abu Musa:  "The Prophet said, 'The example of a good pious companion and an evil one is that of a person carrying musk and another blowing a pair of bellows. The one who is carrying musk will either give you some perfume as a present, or you will buy some from him, or you will get a good smell from him, but the one who is blowing a pair of bellows will either burn your clothes or you will get a bad smell from him.'  (Translation of Sahih Bukhari, Hunting, Slaughtering, Volume 7, Book 67, Number 442)"

Narrated Abu Musa:  "The Prophet said, 'The example of a believer who recites the Qur'an and acts on it, like a citron which tastes nice and smells nice. And the example of a believer who does not recite the Qur'an but acts on it, is like a date which tastes good but has no smell. And the example of a hypocrite who recites the Qur'an is like a Raihana (sweet basil) which smells good but tastes bitter And the example of a hypocrite who does not recite the Quran is like a colocynth which tastes bitter and has a bad smell.'  (Translation of Sahih Bukhari, Virtues of the Qur'an, Volume 6, Book 61, Number 579)" 

Narrated Abu Musa:  "Allah's Apostle said, 'The example of a good companion (who sits with you) in comparison with a bad one, is I like that of the musk seller and the blacksmith's bellows (or furnace); from the first you would either buy musk or enjoy its good smell while the bellows would either burn your clothes or your house, or you get a bad nasty smell thereof.'  (Translation of Sahih Bukhari, Sales and Trade, Volume 3, Book 34, Number 314)"

In the above Sayings, we clearly see how Prophet Muhammad peace be upon him praised the "good smell".  He associated the good Muslims with good smells, and the not so good Muslims with the bad smells. 

http://www.answering-christianity.com/bad_smell.htm

[Md. Siddiqul Alam (Reza)]

The brushing of the teeth:
Our beloved Prophet was also big on cleaning the teeth by the "Siwak":

Narrated Ibn 'Abbas: "I stayed overnight in the house of my aunt Maimuna. Allah's Apostle talked with his wife for a while and then went to bed. When it was the last third of the night, he got up and looked towards the sky and said: "Verily! In the creation of the Heavens and the Earth and in the alteration of night and day, there are indeed signs for men of understanding." (3.190) Then he stood up, performed ablution, brushed his teeth with a Siwak, and then prayed eleven Rakat. Then Bilal pronounced the Adhan (i.e. call for the Fajr prayer). The Prophet then offered two Rakat (Sunna) prayer and went out (to the Mosque) and offered the (compulsory congregational) Fajr prayer.  (Translation of Sahih Bukhari, Volume 6, Book 60, Number 93)"

Narrated Anas:  "Allah's Apostle I said, 'I have told you repeatedly to (use) the Siwak. (The Prophet put emphasis on the use of the Siwak.)   (Translation of Sahih Bukhari, Friday Prayer, Volume 2, Book 13, Number 13)" 

Narrated Hudhaifa:  "When the Prophet (p.b.u.h) got up at night (for the night prayer), he used to clean his mouth.  (Translation of Sahih Bukhari, Friday Prayer, Volume 2, Book 13, Number 14)" 

Narrated Abu Huraira:  "Allah's Apostle said, 'If I had not found it hard for my followers or the people, I would have ordered them to clean their teeth with Siwak for every prayer.'  (Translation of Sahih Bukhari, Friday Prayer, Volume 2, Book 13, Number 12)"
 
Narrated Ibn 'Abbas: "Once I stayed overnight at the house of (my aunt ) Maimuna while the Prophet was with her, to see how was the night prayer of Allah s Apostle Allah's Apostle talked to his wife for a while and then slept. When it was the last third of the night (or part of it), the Prophet got up and looked towards the sky and recited the Verse:-- 'Verily! In the creation of the Heavens and the Earth....there are indeed signs for the men of understanding.' (3.190)  Then He got up and performed the ablution, brushed his teeth and offered eleven Rakat. Then Bilal pronounced the Adhan whereupon the Prophet offered a two-Rak'at (Sunna) prayer and went out to lead the people in Fajr (morning compulsory congregational prayer.  (Translation of Sahih Bukhari, Volume 9, Book 93, Number 544)"

As we clearly see above, our Prophet peace be upon him constantly cleaned his teeth and mouth by using the Siwak. A siwak is a piece of small wood that is approximately as thick as a thumb and as tall as double the height of an index finger.  It's tip is vertically fine-sliced, which means it has wood teeth or hair that is similar to the hair of a tooth brush today, except they are a little thicker.
Obviously tooth paste and tooth brushes didn't exist 1400 years ago.  The siwak with rinsing the mouth was the best and most effective mean to brush off the bad smell and bacteria from the teeth and the tongue, as well as massaging the gums and squeezing out any bad blood from them that may cause tooth aches.
Notice how Prophet Muhammad peace be upon him was very sensitive about not having a bad smell whether from his body or mouth.  Notice also how he was big on keeping the teeth and gums clean and healthy.