I would start looking into sys.dm_exec_query_stats to find the queries that are not behaving as normal per your baseline.

Queries that use a lot of memory must be reading lots of data from disk, so I would start looking for rows with high total_logical_reads / execution_count-

Also, the error you are getting is likely a symptom that MAX_SERVER_MEMORY was not set correctly and both SQL Server and OS are starving. Set MAX_SERVER_MEMORY to a reasonable limit. If you already set it, you are probably getting more multi-page allocations than usual. As you probably know, MAX_SERVER_MEMORY does not limit multi-page allocations and you should be looking for those in sys.dm_os_memory_clerks.

Hope this helps

Gianluca