Multitude of Moving Companies in Ohio. When my job relocated me to a different part of Ohio, I had no problems finding a good moving company. There are so many great moving companies in Ohio. You can research them on the internet, check the local phone book, or even ask around for word of mouth. I did all three. A friend of a friend recommended the company, I researched it on the internet, then consulted my local phone directory for the location closest to me. If you are moving in Ohio, you should have no problems finding a good moving company.