I have a drain in basement about 3 ft in front of washing machine.

I now have order coming from drain and I never had it before.

What are ideas for this issue? Does the wash water drain go to sewer? Or does it goes to sump pump?

This house was built around 1950's.

I guess you mean water is coming up through the drain, right? A 1950s house is anyone's guess but this sounds like a floor drain connected to your sewer. If so, it's the low spot in the system and any back ups would come up through the drain. City or setic? <ost floor drains have a plug that can be removed for rodding, closely inspect with a flashlight and report back. If there is a clean out on the sewer line you could also rod from there but be careful removing any caps or plugs in case there is standing water in the line.

Also... Make sure the floor drain has water in it. If you don't use it on regular bases, pour couple of cups of water into it once a week. This way, you will keep trap wet (filled with water), disallowing sewer gases to enter living areas. If you let trap w/o water, it will become sewer vent, venting into your laundry room.