The loaches and Corys should get along perfectly fine. However, keeping incomplete schools in a tank that is still too small can change that. Again, I know it's not what you want to hear, but the loaches in your 14 is the same exact situation as the Corys in the 6. It's a VERY common situation for people to find themselves in. I would like nothing more than to say "that's a really nicely stocked tank" to people - I don't want to constantly tell people that their tanks are poorly stocked, but things are what they are and in the effort of helping people, it has to be said.
Too, while the 14 is way better than the 6, it's still considered by many to be too small for full size Corys. People can quibble about what the "real" minimum is, but one thing is for sure and that's that they're all minimums, meaning you are providing the very least you can.
I think the best course of action would be to return them all and start over with fish more appropriate for the size tanks you have. If you're not inclined to do that then I would return the loaches and move the Corys to the larger tank. If you're not inclined to return any fish then I guess put the Corys in with the loaches.