Insightly Classic is the old version of Insightly. It's not available to new accounts. Users on Insightly Classic can switch over to the latest version.
List views for contacts, opportunities, and projects can be sorted by clicking the wrench icon above the list and selecting a sorting option.
Other records don't have sorting options for their list views, but you can create custom reports and sort records by any field.
For contacts, you can also select your default for sorting from the User Settings > User Settings page.