Well, at the tender age of 15,, I was introduced to Armadillos while in Florida with the BSA. We were spending a week canoeing, fishing, camping etc in the Central Fl area. The Camp Ranger told us; "If you catch one, we'll clean it & I'll cook it for you. They are tasty."
All week long, us boys tried to sneak up on them, grab them quickly by the tail, and snatch them off the ground. They are strong, can run fast, and if you don't grab one close to the body by the tail, the tail "shell" will come off leaving you holding a hollow tail shell. They can't see very well, but their hearing is very acute.
After a week of trying,, our last night at the camp, the Ranger was cooking one he'd killed already,, since we'd failed. (I'd gotten close and had the tail shell as a Troop souvenir.
Just before supper,, I managed to catch one! FINALLY!!!!!
But I was told to release it, as we had one cooking.
It was VERY good eating.
A year later,,, once again, same camp & all, I was back. I caught one the first night out. I killed it, cleaned it, and cooked it. Simple flour, salt, pepper, & hot cooking oil. First batch,, the boys waited until it cooled to sample it. Second & third batch,, they were grabbing the bite sized pieces from the hot grease to eat.
Yes,, not only are they good to eat, but are very tasty.
3-4 years later,, while stationed at Ft. Hood Tx. I was walking back from the PX,, and spotted a Dillo. Well, he too was caught. Upon entering the barracks,, many a soldier,, especially the minority ones were running & slamming doors to get away from it. I had set it down on the slick tile floor, and it wasn't able to run too fast. But many a soldier did run fast,, all while screaming selective language.

I released that one later too.
They are night dwellers, and as noted,, eat grubs, worms & such. Digging A LOT to get whatever they hear under the soil. They are very destructive to yards & gardens because of the digging.
They have also been migrating to other states. I work in animal damage control, and the State has a mandate for me to report any I see, even road kills.
There are trapping methods, and there are chemicals to kill their food that can deter them from your property. Both require regular work. I know how to build traps, and also how to build stuff to prevent them from enjoying your yard or garden. But often,, either method can be laborious, or expensive.
And many states have strict laws about certain chemicals that are capable of killin the grubs & worms. Many chemicals that are very effective are banned for various reasons.
But,, killing the grubs,, or worms can be the most cost effective method of CONTROL,, but you won't eradicate them fully. Only a barrier around the property, correctly constructed can keep them out.