Do travel agents have to advise and check the visa status including transit visa before selling a ticket?

Check the documentation provided by your travel agent. I guarantee somewhere in there you'll find something that tells you it is your responsibility to ensure that you have the correct documentation for your entire trip, including any visas you might require for any part of the journey.

A good travel agent might volunteer information on what you require, and might even offer to assist you as a service, but the responsibility remains yours.

This is most probably very dependent at least on:

• The specific jurisdiction (country, state, economic zone...).
• Whether the flight was sold alone or as part of a package (together with accommodation, usually, but in some jurisdictions other things like a rental car or activities may count)

In general, it is the traveller's responsibility to ensure they have all the required paperwork, especially as:

• Each traveller's situation is unique. Citizenship, residency, any visas they have, travel history, type of passport, etc. all have an influence, and it can be quite daunting for a travel agent to know all the rules for everyone. Consider that in some cases, even prior travel history may have an influence (e.g. having travelled to some countries will disqualify travellers from ESTA and they must have a "real" visa instead).
• Requirements change over time. Maybe at the time you booked all was well, and 2 weeks later country X decided that citizens of country Y suddenly need a visa. A travel agent can hardly track all of this.
• Traveller situations vary over time as well. A passport expires. A visa expires. Residency changes. And so on.

It is usually expected from a good travel agent that they will inform their customers of requirements that are obvious to them. But even a good travel agent may not be aware of the requirements for everybody. If they are in country X, and all travellers with citizenship of that country don't require a visa to travel to/transit through country Y, then if a traveller from a different country needs a visa, they may not even know it. Most travel agents and airlines will actually inform passengers at length of the most obvious pitfalls, but they can't handle all possible cases.

In your case, I suppose the travel agent was in the US, so their "usual" traveller is probably a US citizen or US resident, who wouldn't need a visa to transit Canada (the US resident may need an ETA, though).

I'd be curious as to the specifics of your travel which would actually required a transit visa, though.

Now, there may be countries with different rules or regulations which require the travel agent to inform the traveller in an explicit manner (and not with a few lines in the middle of the small print) and/or check the traveller actually has the required paperwork, but I don't know one.

Rules may also be different for packaged holidays as opposed to "just flights".

I am personally not aware of any laws, rules, or regulations that require a travel agency or airline to inform passengers at time of purchase about visa and other requirement (but it's possible that in your country or state their might be such a requirement). In my own experience, sometimes airlines or travel agents have done so, and other times they have not. Often, the itinerary and/or e-ticket receipt has a notation advising passengers to check the requirements for the countries they are entering or transiting, but these may be ignored by many passengers.

Your situation is unfortunate and certainly a horrible experience, and I hope the airline was able to reschedule or reaccommodate you after you obtained the transit visa.

It's mentioned in the various documents which they provide you. Probably more than once. Probably emphatically.

At least one of those documents will be a contract. Contracts are an agreement between two people. ("People" potentially being a corporation). An agreement means you keep your word. They write the contract, but if you agree, it's your word. Obviously to keep your word you have to know what your word is, which obliges you to read the contract.

Of course in modern life you see long contracts on a daily basis - I just signed one when I installed a computer game - you signed one when you joined StackExchange. Or that book they give you with every prescription. It's overwhelming. Some people respond by not reading any paperwork at all, and just taking their chances.

I hate to say it, but this is that.

On one hand, if you were new travelers, the agent should have mentioned this more... but it may have slipped your mind among the many, many things discussed. On the other hand, if you live in an area where most flights to anywhere involve a bounce through North America, this is something you need to know.