Context clues refer to the surrounding information of an unknown or unusual word we find in a text when we are reading that helps comprehend the meaning of that word.
To find the meaning of the term "onerous," then, we must look at the surrounding information of that word. First, the speaker mentions that they returned home late after a tough day at work and continue with the word "but" that help us infer that what's coming next is the opposite of resting, then the speaker uses the verb "forced" which also has a negative connotation, and last he mentions a task that involves physical effort: cleaning the kitchen.
From all this information, we can infer that "onerous" means something that is burdensome, oppressive or that involves a great amount of effort.