A‛oodhu billaah
A’oodhu billah is to show Allah (subhanahu wa ta’ala) I’m weak and you are powerful. It is to seek guidance and seek protection. A’oodhu can only be followed by the name of Allah (subhanahu wa ta’ala). If A’oodhu is followed by any other name then it is equivalent to giving that entity the status of Allah (subhanahu wa ta’ala), which would be shirk.
Shaytan
Shaytan is the being that is far-removed from the mercy, righteousness, piety, straight path etc. of Allah (subhanahu wa ta’ala). Shaytan is not one being. (that is Iblees, head of Shaytan). Shaytan is a generic term that applies to every entity human (those men who are preventing you from praying, those men that are calling you to worship someone else besides Allah (subhanahu wa ta’ala)) or jinn that are removed from the path of Allah (subhanahu wa ta’ala).
Hadith from Sunan an-Nasa’i
It was narrated that Abu Dharr (radi allahu anhu) said: “I entered the Masjid and the Messenger of Allah (sallallahu alaihi wasallam) was there, so I came and sat before him and he said: ‘O Abu Dharr, seek refuge with Allah from the evils of the devils among the Jinn and mankind.’ I said: ‘Are there devils among mankind?’ He said: ‘Yes.’”
Rajim
It is an adjective describing Shaytan. Ar rajim means the one that is cast away(pelted with stones) i.e. expelled from all types of righteousness. Thus, Shaytan by his nature is far-removed and by his actions he is cast away.
As-samee‛-il-‛aleemi
As-samee’ and Al-’aleem are the names of Allah (subhanahu wa ta’ala). These two names are picked for very specific reasons. When a jinn whispers into our ear, we do not hear, but As-samee’ hears. And with Al-’aleem we are indicating our sincerity with which we are turning towards Allah (subhanahu wa ta’ala).
Hamzihi
It comes from the root word Hamz, which means to prod or to poke or to push for doing something. Shaytan is continuously trying to prod us to do something bad. So we seek refuge from the hamazaat of Shaytan.
Nafkhihi
Nafkhihi means to blow. Shaytan is continuously blowing into us in ways we do not know. So we seek refuge in Allah (subhanahu wa ta’ala) from the nafkh of Shaytan.
Nafthihi
Nafth is to blow with a little bit of spit. Shaytan is continuously blowing at us with a little bit of spit. So we seek refuge in Allah (subhanahu wa ta’ala) from the nafth of Shaytan.