Yes you can. You can't travel back to your home country, otherwise you can use your old passport along with refugee travel document as long as the visa is valid.
After your refugee application is approved, you can request to have your old passport back. U.S visas are not automatically canceled the moment you apply for asylum in Canada. Most information here is not valid.
If U.S. cancels your visa they will contact you, but you can always call the U.S. embassy and ask for validity of your visa if you got the document number of your visa and you should do that before trying to travel to U.S.
The law above is interpreted in a wrong manner. If you RENEW the passport of the country that you sought asylum from, or reapply for a new one yes your refugee status can get canceled. But requesting your passport back because you have valid visas for other countries , and using those visas to travel to said countries, while using RTD is perfectly okay. You shouldn't renew your passport even if it expires.
U.S. lets you use the visas in your old passports thats past its validity, and U.S. issues visas past passport validity due to this (They will issue 10 year visa, even if your passport expires in 7 years for example, so you can use your old passport and a RTD past its validity, despite passport expiring the visa on it is still valid).
Requesting your passport back from IRCC is not the same as renewing or obtaining your countrys passport. So if you get your passport back, and get a RTD and use the visa on it to travel to U.S., it is no problem. If you renew your passport, or get another passport from your home country it will lead to cancellation of your refugee status in Canada (not always enforced but that is the law). You should still not use your old passport as a main traveling document, always accompany it with a RTD.
As for comment above, Five Eyes countries share exit / entry information. Other countries do not share information with Canada or the U.S. (perhaps there are exceptions but EU doesn't, but has a shared information system within. Same for GCC countries and ex-Soviet ones). So the U.S. already knows you applied for asylum in Canada, if you get questioned in U.S. just explain the situation about you having a visa previously and sought asylum in Canada, they will check validity of your visa and decide whether to let you in or not.
The U.S. as far as i know only cancels their Visas, if you break the terms of visa. For example, using U.S. visa to enter the U.S, then traveling to Canada illegally to claim asylum there breaks its conditions. In that case you should not get asylum in Canada due to safe third country agreement anyway but current administration of Canada grants asylum anyway, this however breaks the terms of U.S visa and your U.S. visa gets canceled. However if you hold Canadian visa and U.S. visa seperately, and have never broken terms of U.S. visa before and claimed asylum in Canada directly, then it is up to U.S. discretion to cancel the visa or not (they usually do not.).
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