We know that the Quran contains no contradictions, but I want to know what the Quran means when it says these three things about Prophet 'Eesa (Jesus), peace be upon him:
He is: the word of God, the spirit of God, created from dust.

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.

The meaning of ‘Eesa (Jesus)  being the Word of God is that he came into existence by the Word of Allah "Be", as was stated by the interpreters of the Quran among the Salaf (righteous predecessors). Imaam Ahmad said, “It [i.e. the creation of ‘Eesa] was with the word that Allah sent down to Mary (Maryam) when He said to him: (Be) and ‘Eesa was (i.e. came to existence) with the word ‘Be’; Allah says (what means): {Indeed, the example of ‘Eesa to Allah is like that of Aadam (Adam). He created Him from dust; then He said to him, 'Be,' and he was.}” [Quran 3:59]

The meaning of ‘Eesa being ‘the Spirit of God’ is what Al-Baghawi said in his Tafseer: 

“And he is a soul like all other souls, but Allah added it (attributed it) to Himself as an honor (for 'Eesa). It was also said, 'The Spirit was the blowing which Jibreel, may Allah exalt his mention, blew to the garment of Maryam and she became pregnant by Allah’s Will. The blowing was called spirit because it is a wind that comes out of a spirit, and Allah attributed it to Himself because it was with His Order.'

It was also said, 'The Spirit of God means His mercy, so ‘Eesa, may Allah exalt his mention, was a mercy to those who followed him and believed in him.'

It was also said: Spirit means revelation; glad tidings were revealed to Maryam, and the command to blow was revealed to Jibreel (Gabriel), may Allah exalt his mention, and the command to 'Be' was revealed to ‘Eesa and so he was. Allah says (what means): {He sends down the angels, with the inspiration (rooh) of His command}; meaning with revelation. And it was said: what is meant by spirit is Jibreel, may Allah exalt his mention; so the meaning is: and His Word which He delivered to Maryam, and He also delivered a spirit to her with His Command, who was Jibreel, may Allah exalt his mention; as Allah says (what means): {The angels and the Spirit descend therein} [Quran 97:4], meaning Jibreel descends therein, and Allah also says (what means): {Then We sent to her Our Spirit} [Quran 19:17] meaning: Jibreel.”

Ibn Hajar said:

“Allah described him (‘Eesa) as being from Him; the meaning is that he existed (as a favor and kindness) from Him, as Allah says (what means): {And He has subjected to you whatever is in the heavens and whatever is on the earth - all (as a favor and kindness) from Him.} [Quran 45:13]; that is to say that Allah subjected these things which existed (as a favor and kindness) from Allah: He is the One Who made them and Who brought them into existence, with His Power and Wisdom. Adding (attributing) specific things to Allah is of two kinds: Firstly: to be attributed to Him because He created them and brought them into existence; this encompasses all creatures, as you say: the land of Allah, the sky of Allah. Secondly: to be attributed to Him because of the specific meaning that Allah allocated to it, a meaning which He loves, orders and is pleased with; like calling the Holy Mosque in Makkah 'the House of Allah' since there is special worship performed therein that is not performed in any other mosque; this is the same with ‘the Word of Allah.’”

It is not mentioned in the Quran that ‘Eesa was created from dust; rather, the Quran mentioned that our father Aadam, may Allah exalt his mention, was created from dust (clay), or that Allah created the human being or the people in general from clay with the fact that their father Aadam was created from clay, as in the verse in which Allah says (what means): {It is He Who created you from clay and then decreed a term and a specified time [known] to Him; then [still] you are in dispute.} [Quran 6:2]

Allah also says (what means): {And certainly did We create man from an extract of clay.} [Quran 23:12]

Allah further says (what means): {Who perfected everything which He created and began the creation of man from clay.} [Quran 32:7]

As regards the saying of Allah in resembling ‘Eesa with Aadam: {Indeed, the example of ‘Eesa to Allah is like that of Aadam. He created Him from dust; then He said to him, "Be," and he was.} [Quran 3:59]; what is meant by the resemblance here is that He created him without a father, as Aadam was created without a father or mother.

Al-Qurtubi said, “The resemblance is that ‘Eesa was created without a father like Aadam, and not that ‘Eesa was created from dust. Indeed, something may be likened to something else even though there is a big difference between them if they have one same characteristic; Aadam was created from dust while ‘Eesa was not created from dust, so they are different in this regard, but Allah likened them because He created both of them without a father.”

Allah knows best.