First I want to mention the similarity of "äu" and "eu". You could say that "Hoiser" would be a better fit than "Häuser" (because of the sound), but if you look at the (written) singular "Haus", then it is more understandable to use "äu" instead of "oi".
But how did it develop: According to "Die Entstehung der neuhochdeutschen Schriftsprache" (pages 132, 133) we first had the "ou" sound:
frouwe (Frau, woman)
Around 1350 this started to change to "au":
frauwe
This "au" was also used in combination with "w" ("auw" or just "aw"):
nauw (neu, new)
getrawer (Getreuer, follower)
From 1485 this was changing to "ew", "euw":
neuw
getrewer
and from there it was a small step to "neu"/"Getreuer" as we use it today.
From "ou" to "au" was a coherent step, because they sound similar, "oi" would be not an option here. Then the development changed to "eu", not only because it sounds similar (maybe especially in the 15th century), but because of its similarity in the written language. This written similarity I wanted to show with my "äu"-example in the beginning, because language develops on both paths, written and spoken, simultaneously.