I have seen a few grasshopper-looking bugs in my unfinished basement, a few venturing into the finished side. I have been using my kids’ butterfly net to catch and remove them, but that method is not reliable.
Short of bringing in toads, how does one remove/kill katydids or grasshoppers from the home?
I don’t have anything useful to contribute, but I must share that just yesterday I had 19 crickets (my gecko’s dinner for a few days) escape and disappear under furniture. Maybe they found your place?
Well, where else to look but a good marijuana growing article to find out how to rid those nasty disease carrying man-eating grasshoppers from your house.
But really, why can’t you just leave the things alone? I have lizards running all through my house but you don’t see me trying to get rid of them. Damn humans trying to ruin the ecosystem.
grasshopper-looking bugs in the basement are usually identified to be Cave Crickets/Camel Crickets. Apparently they can be controlled by the introduction of House Centipedes, but for some reason many people do not find this a desirable solution.
That is what we have, a shop vacuum and a strong flashlight is the best method of hunting them. I do this every spring and it keeps the population from getting upstairs. Many house cats will also hunt and eat them. Unfortunately, many house cats do not. Damn worthless cats. 
Good luck, they cause no harm and make interesting show and tell items for your kids to bring to school. They mainly live on mold in the dampest part of your basement, garage, crawl space or shed.
Jim
so, my options are as follows:
Silly me for thinking this would be easy!
Are your critters indeed cave crickets?
The Flash light and Shopvac can be kind of fun. Just watch out these critters have the disconcerting habit of jumping at you instead of away from you. They cannot hurt you, but the first time you experience this, they could cause you to shriek like a little girl. 
Jim
I grab grasshoppers by the back legs at the joints that stick up above their back. This prevents the tobacco juice from getting on your hands. So named by farmers because of the spitlles color. Then I whip them into a hard surface. They’re now dead or dying. You can crunch them inbetween two stones if you like, or if you want to practice for television between your teeth. Capture is the same for all disposal methods. You may get lucky and catch two at a time when they have their abdomens stuck into each other reproducing. Even a child can catch them then.
I know that a lot of insect nerve agents like Raid Ant & Roach spray (I believe the culrpit agent in this case is Propoxur) will kill crickets fairly quickly. It’s a very unfriendly approach but a single spray within a foot or so of the cricket is going to kill it within seconds. Simply spraying around a little might be sufficient to keep the crickets at bay.
However, is there anything they are doing that actually bothers you? You could try introducing some large spiders but it sounds like you don’t want to go that route. Maybe you could just co-exist peacefully?
Geez. You all make it sound so complicated. I just lay down one or two sticky traps in strategic areas – like in a doorway from the room with the water heater to the area of the finished basement – and after a few weeks, they’re pretty much gone.
I don’t know, between being crushed, eaten, poisoned or dying slowly of dehydration while stuck to the floor, which seems the most cruel? I think a lot of people have a natural aversion to sticky traps simply because the comparable weapon for humans would be much more terrifying than nerve gas or being crushed by a giant foot.
Cave Crickets eat Mold and other Fungi, check the Ops name, I would be worried too.