I use it a lot for a blog I do that covers the world. I have to search for news in other languages and I have to say that it continues to improve. There will always be difficulties in translations. I did a literal translation once in my head in Czech that makes people crack up. I knew Cow, eat, and grass. I said Krava ji trava which translates perfectly in Google. But for four years I've constantly heard... "Say it again!" from Czech people. It's completely incorrect structure and tense. At least it gets a good laugh.
You're right - that is bad. What English speakers who don't know Japanese may fail to understand is that this expression isn't used, for example, after someone sneezes. (The Japanese generally don't say anything after someone sneezes. If anything, the person who does it may apologize.)
Instead, odaijini is used when you learn that someone is sick, for example, with a cold. You might say it to them as you say goodbye. Nurses or receptionists at clinics often say this to you when you leave, even if you aren't actually sick (e.g., if it's an IVF clinic).