select nodes title start with charachter
There is no database agnostic support for regex in EntityFieldQuery. The documentation in EntityFieldQuery::propertyConditon lists the available operators. As mentioned by Clive, this list is not complete. Apparently you can use any operator that is supported by your database backend.

As an alternative that should be supported across different database backends, you could build multiple queries using the STARTS_WITH operator and then merge the results.

Or you write a custom query using db_query. Or use db_select with or-linked conditions.