Are you ineligible for DACA?
Canada doesn't necessarily care about your lack of status in the US, but they do prefer people apply from their home country as you would need to convince them you'd return there after your visa expired; obviously you wouldn't be able to re-enter the US without some form of advance parole.
Getting a work permit would be difficult as an employer would have to prove no Canadians could do the job before sponsoring you. Studying is easier but costs money, albeit not as much as in America. You might want to consider
two-year colleges in Ontario. You can work part-time as a student and potentially full-time after graduation in order to qualify for permanent residence.
For information on your options, visit
cic.gc.ca and
educanada.ca.