Okay, I'd love to build a smallish adobe wall, but here's the thing: I've only done it as a kid a looooooooooooooong time ago, and to be honest, I remember the process, but not the "recipe" for making adobe bricks that actually last.
adobe ( & cob ) are both made of a mix of clay & sand & water & straw. There's some good cob books around like one by becky Bee whose title I can't remember. Probably a good place to start. It has recipes in & all sort of tips & pointers.
Making cob or adobe last on a wall, you need to protect it from the elements. It will need a good foundation & a little roof possibly. Unless if is somewhere sheltered. You can earth plaster it with lime in the plaster to help protect it too. I would avoid putting cement in the mix.
If you want to do an adobe wall, you'll need to make a mould for your bricks & leave them to cure for a while before laying them.
I should know, I live in adobe-ville- New
There are actually seveal recipes and each has different strengths and weaknesses.
My house is adobe and is made from the clay-soil that was dug out from the crawl-space. They added some straw and some even have a bit of rock in them. I think in the old old days they may have even added manure.
I do know that adobe is not as warm as straw-clay since adobes have less straw in them.
I've built with both straw-bale and cob but never adobes which seems crazy.
Search on adobes brick recipes and see what you come up with.