How to understand the teachings of Jesus if both Christians and Muslims say the same thing about him? Also, Jesus says that, "I am the One, the Way, follow me." What is the Islamic explanation for this?

I will not try to interpret the Biblical passage because once we step into that slippery slope, we can have millions of different possible interpretations.

Jesus said "I am One", as also said to the disciples that, "You and I are one."[1] So, this concept obviously is not to be taken literally. It is a figurative statement, "one" in Will, that the Prophets followed, the Will of God,[2] as examples stated in the Qur'an,

" مَّن يُطِعِ الرَّسُولَ فَقَدْ أَطَاعَ اللَّهَ"

"He who obeys the Messenger, has indeed obeyed Allah."[3]

And this is our belief, those who obeyed Jesus, obeyed God. They were "one" in terms of will. Jesus submitted to the Will of God and there are many statements to that effect.

The other statement, i.e, "I am the Way.", all the Prophets were the way. Each Prophet, which you can even find in the Old Testament (eg: Moses), says that Prophets bought the way.

In Islam we have to believe the Qur’an and the Sunnah, which is the way of the Prophets. All the Prophets when they came identified the way to God. The truth is that the teachings that Jesus brought were the embodiment of truth, and that is the same which Muhammed (ﷺ), Moses and all the other Prophets brought. In following that way in truth, you would attain, ever lasting life, in Paradise.[4]

References:

[1] John 14:20

[2] Dr. B. Philips, The True Message of Jesus Christ, p 49-50

[3] Surah An-Nisa’, 4:20

[4] B. Philips, Did God Become Man, p 5-9