Can someone please show me how the Latin Iesus came from Iesous? It sounds like a shorter form of it. Is it just because certain sounds from the Greek wasn't in Latin?
Looking back at this, it seems like a simpler answer might be more appropriate, but my other one's been seen enough I don't want to completely gut it.
Basically, every sound in "Iēsūs" exists in both Greek and Latin. But neither Koine (Biblical) Greek nor Latin had enough letters to represent all of their vowel sounds. Both languages had twelve individual vowel sounds, not counting combinations like "ae". But Latin had only six letters for them (a e i o u y), and Greek seven (α ε ι ο υ η ω).
So Latin spelled both the long and the short vowels the same: the long marks I'm using weren't common in Classical times, and ū and u would usually have been spelled just the same.
Greek did that too, for some vowels: they didn't distinguish long and short alpha, for instance. But in other cases they used two letters together to represent a completely different sound. And in particular, ου was pronounced like Latin ū.
The reasons for this are harder to explain (see my other answer for the details) but basically, when you run out of letters, using combinations is a good way to get more mileage out of the alphabet you have. Consider how English uses "sh" for a sound that's not the same as either "s" or "h".
So Iēsūs and Ιησούς were pronounced pretty much the same, except that the Greek was accented on the last syllable (see the accent mark) and the Latin wasn't.
However, there were actually two sounds lost in the translation. The Biblical Hebrew version of the name was Yēšūaʕ, where š is the first sound in "ship" and ʕ is a sound English doesn't have. And neither Koine Greek nor Latin had these sounds. So š turned into s, and ʕ just disappeared.
The consistency of Greek spelling tends to hide the sound changes that happened within the language. Greek originally(*) had three different "o-like" sounds, written ο, ω, ου. Since they had only two "o-like" letters, they needed to use two letters together for the third one. The same thing happened with their three "e-like" sounds, ε, η, ει.
It's thought that these originally corresponded to the sounds /o ɔː oː/, which would be written as o ō ō in Latin, which only had two "o-like" sounds. Similarly, ε η ει were /e ɛː eː/, e ē ē in Latin.
But in later Greek, ου shifted to /uː/, and ει shifted to /iː/. So these sounds were then written as ū and ī in Latin. (Compare how ou is pronounced as /u/ in modern French.)
Iēsūs was then the best way to transcribe the Greek word into Latin, matching the sound of the Greek word as closely as possible.
(*) As fdb quite rightly points out, "original" is a tricky word to apply to Greek. I'm referring here to the Attic dialect, at the time when it was first recorded in writing; this is the dialect that eventually became the Koine used in the New Testament, and (much later) the Modern Greek of today.