What is the legal status of travelling with (unprescribed) methadone in your carry-on?

It is not legal to bring methadone into Canada without a prescription.

Methadone is a controlled drug in Canada under the Controlled Drugs and Substances Act (it's in Schedule I, number 5 (4)). It is illegal to import a controlled drug into Canada without authorization (section 6, "Importing and Exporting"). The maximum punishment is life imprisonment; I suspect in practice the punishment would be less, but I don't know how much. It probably wouldn't be good.

There is an exemption that can apply for prescription medications for a traveler's own use, but since the drug was not legally prescribed to your girlfriend or her sister, the exemption does not apply.

If they declare the drugs at Customs, the drugs will certainly be confiscated, and they may or may not be punished. If they don't declare them, their luggage may be randomly searched, and if caught they will almost certainly be punished.

I am going to assume you want to advise them on the correct and legal behavior, not help them circumvent the rules.

First, medications are exempt from the 100ml rule and everyone advises you keep your meds in carryon. (For example, here's the advice for Canadian travellers.) It should have a label that identifies it. I have never been asked to show a doctor letter or other paperwork for prescription meds, but in theory you should have this too. If the label identifies it as medication, being over 100 ml should not be an issue. Of course if it is in some sort of unlabeled container, there is going to be problem with that. This will apply when leaving Ireland, clearing security to get on the plane. I suppose if it says something on the label that gets the agent's attention, they could call the local police, but their focus is really on making sure nobody blows up the plane.

Second, while many people put all sorts of things in their checked luggage without consequence, this doesn't mean that there is no problem bringing things into countries where they are controlled. There are xrays and such that are on arrival to look for things like drugs in people's bags. There are sniffer dogs in the arrivals area, and trained border agents who send people to secondary for more inspection. If this methadone had been prescribed to your friend, then bringing it would be ok if

The drug must be for your use or for the use of a person who is travelling with you and for whom you are responsible. The drug must be in hospital or pharmacy-dispensed packaging, the original retail packaging, or have the original label attached to it clearly indicating what the health product is and what it contains.

(A quote from the link above.)

If it's just in some sort of jam jar with no label, there's going to be a problem. Smuggling opiates is non trivial. Hoping to get away with it is not a strategy. If the friends are unable to get any methadone prescribed to them, and unable to function without it, then the trip is a bad idea.

There are a whole string of violations here.

• Failure to Declare the medication. It is a crime to fail to declare anything on a long list of things you need to declare, and you bet medicine is at the top of that list. The only way out of that one is to declare "Yes, I have methadone in my bag". Otherwise if you're caught, it's big trouble, a big fine, and you will not be visiting Canada anymore. But if you admit to having it, you evade that charge but not these:

• Possession of methadone without a prescription. That itself is a crime even if they were not crossing an international border.

• Importing drugs into Canada. Obviously, trying to import narcotics into Canada is a serious felony, so they will get to be the guests of the RCMP for a number of years, and will not successfully visit any other countries for the rest of their lives, because they'll be in all the databases as a convicted felon.

And your girlfriend will be neck deep in this if she is connected with the friend at all. And she will be connected with the friend because young people can't stop using social media, and will be shown to be fully cognizant of the plot (and thus an accomplice). The texts will be found. This SE post will be found. Everything will be found. Cops are very good at police forensics, young people are very bad at it, and drug use doesn't help. International authorities tend to regard friends traveling together as mutually culpable.

Also it is possible for drug users to entangle other people into their schemes.

Your girlfriend's best bet is to either not go, or find a pretense to travel separately. Both ways.

Your best bet is making sure not to travel with them.