You should be able to use your Laser card online anywhere that accepts Laser. However, its Maestro function does not work online.
In the UK the old Switch Debit card system was rebranded Maestro, however it does not accept non-UK Maestro cards. So, you would not be able to use an Irish Laser/Maestro card on a UK site.
Nor, could you use a UK Maestro on a German, Irish etc site.
But, if the site's displaying the Laser symbol and accepts Laser, you should have no problem using your card.
Many Irish sites accept it, e.g. buy4now etc.
As does Worldpay.
You can also use your Laser/Maestro card in many retail outlets outside of Ireland where the Masetro logo is displayed. It works just like it does as a laser card, with your chip and pin.