I will be travelling soon from Delhi to Washington DC with a 3 day stay in Dubai. I don't want my checked in luggage during my stay at Dubai, can I check in the luggage from Delhi to Washington DC even there is 3 day stay in Dubai?
No. The baggage system is not designed to store luggage for this period. You should arrange to store your bag in a left-luggage facility.
If you have concerns about customs controls for alcohol, pork, et c., there is a procedure whereby Dubai customs retains these items and return them to you when you leave the country again.
I would suggest to check with the Airline as some airlines (Ex. Emirates) does make arrangements as they are the official carrier of UAE an would most welcome any traveller to stay (as it's good for UAE's economy and promote tourism)