Hello I live in Ohio. I plan to go China in July for participating in a conference? Can I apply China VISA through the Embassy of the People’s Republic of China at Washington DC? If not, please suggest me the consulate office I need to go.

Also, if you're in Chicago, the Chinese consulate in New York would be in charge of your case (china-embassy.org/eng/zmzlljs/t84229.htm). You can complete your application requirements & show up in person, or hire one of the many agent services to do this for you.

You don't go to the embassy. You go to the Visa and passport office. Make an appointment online and you should be able to go and get your visa in the same day.