How do you check if a string contains any strings from a list in Entity Framework?

You can try using Any method, I'm not sure whether it's supported but it's worth trying:

var result = context.Data.Where(data => searchTerms.Any(x => data.Name.Contains(x)) ||
                                        searchTerms.Any(x => data.Code.Contains(x));

If this gives you NotSupportedException you can add AsEnumerable before Where to fetch all records and execute the query in memory rather than DB.

I'm late to the party but using the SearchExtensions nuget package you could do something like the following

var result = context.Data.Search(x => x.Name, x => x.Code).Containing(searchTerms);

This builds an expression tree so will still perform the query on the server (and not in memory) and will essentially run the SQL you desire above