The pods do pose many questions but all the honey locust I know have smooth bark. This one has flaky bark.
Assuming the OP does know a crab apple from a carob the process for cuttings is quite straight forward.
Most apples are relatively easy to strike as cuttings but ability to root does vary from one type to another. A couple of my crabs have been quite difficult from cuttings.
Take pieces of relatively young wood if possible. Older branches can root but new shoots are quicker and more reliable.
Your crab apples will be dormant this time of year so no leaves to deal with. Dormant cuttings are slower but much more reliable than summer cuttings. Check for pests and diseases. No point taking cuttings covered in woolly aphid. If there's any doubt about pests or disease the cuttings can be dipped in peroxide solution or bleach solution to kill most bugs.
Cut into sections about pencil thick and 10-30 cm (4-12") long are good. Lower cut close below a bud is best. Make sure you know which is the base and which end is the top as they don't grow well upside down. Some use a different cut - straight across or slanting - to keep track of which end is which but you can usually tell by the shape of the dormant buds.
Rooting hormone (from the plant nursery) does help with rooting but you should still be able to get good results with apple without treatment. Follow instructions on the pack to dip the base of each cutting.
Most people then plant the cuttings right side up in a propagating mix (available at the nursery or make up from peat/sand/ perlite) in pots and place in a semi shaded area if possible. Water as the mix dries out. I have had some issues with dormant cuttings like this dehydrating over winter and failing to root. A plastic bag over the top may help but can occasionally promote fungal infection.
Alternative method from the old days is to tie cuttings into bundles and bury them in the ground over winter. The ground protects the dormant wood from dehydrating but you do have to remember where you put them! In early spring dig the bundles up and check the base of the cuttings. Many will already have callus which is the start of root production. Untie the bundles and pot cuttings into pots of propagating mix, potting soil or straight into the ground. Again, make sure they are right side up. For the few weeks in spring until roots form they should not need covers for humidity.
Dormant apple and plum cuttings can even be planted straight into a bed in the ground and some will usually grow.