How can I quickly remove all of my data from my device and then get it back again? Soon, I'll have to give my phone (a non-rooted LG Nexus 4) to another person for some time. As the phone contains very sensitive information, I do not want this person to be able to access any of it. Unfortunately, I don't have data encryption turned on, so I can't just turn the device off and be sure that the other person won't be able to decrypt it.

Basically, I want to wipe my phone right now and then restore it to exactly the state it was before the wipe.

Therefore, I was thinking of backing up my device completely, wiping it and then restoring the backup. How can I do this? Will adb backup -all -shared -apk be sufficient? I guess not, since I'm afraid there are some settings that adb won't detect. Is there a lower-level way, like making an image of all the phone's memory with fastboot/recovery or something?
You would need to root your phone and install a custom recovery in order to make a nandroid backup of your entire system.  There are YouTube videos on how to do this. Please remember that there are risks in rooting and in flashing recoveries.