How do those who believe that Jesus is a created being understand the verses which say everything that was created was created by him? There are some people who claim that Jesus is a created being, but this claim is nowhere confirmed, rather the Bible says:

Everything became through the Word, and without the Word did not
become one that has become. (John 1:3)
From him and through him and for him are all things; to him be the
glory for ever and ever. Amen. (Romans 11:36)
Colossians 1:15-16 (NIV): The Son is the image of the invisible God, the firstborn over all creation. For in him all things were created: things in heaven and on earth, visible and invisible, whether thrones or powers or rulers or authorities; all things have been created through him and for him.

I mean, that's pretty obvious.
So if the Bible says that everything was created through him, how is it possible that he is a created being? Did he create himself?
Warning: These are not my own beliefs, but I also don’t believe in straw-manning so this is only my best attempt to describe in their strongest form, what I might believe if were an Arian.

I think the argument could be made that Arianism and semi-Arianism try to grapple with just these texts. Taking their cue from Colossians 1:15, Arians and semi-Arians both deny Christ is homoousios with the Father - they reject the idea that he is the exact same, un-created substance and instead argue he is the uniquely first among created things. In the Profession of Faith of Arius Arians confess this about Jesus:


  He who has begotten the only-begotten Son before aeonian times (χρόνων αἰωνίων), through whom also he made the aeons and everything, who produced him not in appearance but in truth, giving him existence (ὑποστήσαντα) by his own will, unchangeable and unalterable (ἄτρεπτόν τε καὶ ἀναλλοίωτον), a perfect creature (κτίσμα) of God, but not like one of the creatures, a product (γέννημα), but not like one of the things produced (γεγεννημένων)...


Four relevant observations can be made from this: (1) Jesus is begotten before the creation of everything else, (2) in fact before time itself, (3) it is through him that God made time and everything, and (4) although a creature Jesus' creation is not like one of the other creatures, and although a product he is not like any other thing produced.

According to Arius then, Jesus is a sort of 'third thing' unlike the un-created Father, but unlike anything else created in time including time itself. Here is how they might interpret the verses you cite:

John 1:3 Your translation uses the word "become" which makes this verse a slam dunk for an Arian. Becoming involves change or creation in time. While Jesus was created, he was done so in a uniquely nontemporal way. Therefore, Jesus is not something which became, but existing prior to what has become, he can - without difficulty - be involved in the creation of all of it. Even with a different English translation, the greek word ginomai can by an Arian always be translated to involve the creation of things in time.

Romans 11:36 This verse doesn't, on first observation seem to refer to Jesus specifically, the him being a reference to verse 33's use of theos. So I don't think an Arian would be easily forced to thing of this as a reference to Jesus. Although perhaps it is a cross-reference to point out Jesus is referred to in other passages in the exact same way God is being referred to here. Still, an Arian can say this is about God and that similar passages can also be about Jesus since according the the Arian profession of faith:


  ...the Father gave him the inheritance of everything...


Colossians 1:15-16 It has already been pointed out that this passages seems to support the unique creation of the Son. It is then a matter of reading from the text to feel inclined to interpret verse 16 as including the (uniquely created) Son in the creation of all other things. The exception seems to be demanded by verse 15.

An even stronger explanation for these passages can be fielded by the semi-Arians such as are represented by the 359 Creed of Nike - many believe Sir Isaac Newton was a semi-Arian. They were homoiousians meaning they rejected both the Arian claim that Jesus was unlike the essence of the Father and the Orthodox (homoousios) view that Jesus and the Father are of the exact same essence. The Creed of Nike can affirm belief


  ...in one only-begotten Son of God who before all ages and before all beginning and before all conceivable time and before all comprehensible substance (οὐσίας) was begotten impassibly from God through whom the ages were set up and all things came into existence, begotten as only-begotten, sole from the sole Father, like to the Father who begot him, according to the Scriptures, whose generation nobody understands except the Father who begot him.


Semi-Arians believe Jesus was of 'like' not the 'same' substance as the Father. Here Christ is described as being created impassibly. Impassibility is a term used only of God an comes from negative theology which tends to emphasize God's inability to change or be change, be created or 'caused' in any sense to become. This tells us something about the way Jesus was made uniquely different from the creation of anything else, and at the same time tells us "nobody understands except the Father". This clarifying that Jesus' creation was 'creation' in a sense we are not capable of understanding means that it is only natural to include exceptions for Jesus when dealing with the creation of things we refer to as being 'created'.

In the end, Jesus' being created before time, in a way different from all the rest of created things, allows an Arian to involve him in the creation of "all things" because "all things" shouldn't include Jesus.