Is there any way to search for a home based on size of living room or dining room?

No. Since there are no rules as to how people use each room in their house there is no way to search for such parameters. But when considering houses built within the the past 20 years you often can by identifying the living room as a "great room". Great rooms imply a larger size and the label is often used when there are more than one living rooms designated in the house. I hope this helps your search. FYI, don't be afraid to call the Realtors of the houses you like to verify room sizes before you take the time to see the properties. That is their job to do. Good Luck.