I think I'd need more context, because of the too. To me, it sounds like "and from that point on, the proceeded like (whatever too is in reference to). Generally "off they go" means something like . . . a person starts to do something very predictable, very single-mindedly. Hard to explain.

It is said when something bad starts happening again. Here husband and wife start quarrelling again. In fact, two better expressions to use are "here we go (again)" and "there they go again". They mean the same thing as "Off they go, too" which is a little awkward and not so correct. The "too" is particularly awkward. "Off they go again" would be more natural and native. "To go off" means to explode. For example, the bomb went off, killing 20 innocent pedestrians. Two people can explode and have a row. Off they go again!

Yes, it sounds to me like it means that they began to argue also. The paragraph starts with "Or down the block a husband asks his wife..." so it sounds to me like in a previous paragraph they described two or more people at the other end of the block / neighborhood. Perhaps those people also got into an argument and that's why the author included the word "too" in "And off they go, too." It also sounds to me like it could mean that they left the house to go somewhere though. "And off they go (to the store), too." for instance. So it would depend on the paragraph before this one. :) In other contexts, "And off they go." can mean other things. For instance, at a horse race, it would mean that the buzzer sounded and the horses started running. For instance, "The buzzer goes off and off they go down the race track..." The same can be said of children running out of a school to go home when school gets out. For instance, "The bell chimed 5 p.m. and off the students went to their homes to enjoy the rest of their day free of classes and schoolwork."

So, I actually googled the above and found the article on line. Some phrases: "they're off!" - usually said at a race. Horse race, dog race. "off we go!" - usually said at the beginning of a trip, or an errand or a task. "off they go!" (1) can mean "they're off" above "off they go!" (2) can mean same as "off we go!" but talking about third person. For example: Parents might say to each other, while watching their kids leave for college" "off they go!". "off he/she/you/they go!" (3): as i described below "to do something very predicable, very single-mindedly." Typically the speaker is a little amused or annoyed/frustrated. "Every time my wife hears about a shoe sale, off she goes, shopping and spending money, and I can't stop her." "Every time my husband's favorite baseball team plays, off he goes to the stadium" So, that's what's generally happening here. The context is family arguments. Sometimes couples, like husbands and wives will frequently bicker at seemingly stupid things. But note the use of the word "too." It means "also". So, here, what the author is saying is not just that the couple is starting to "go off" and argue, very predictably, very single-mindedly, but that, in addition, this second example of "going off" is like the first.

The previous paragraph: It could happen like this: As they settle down in the evening to watch TV, a wife says to her husband, "The clothing store called. They have the snow suit in Michael's size. Could you pick it up tomorrow? You drive right by the store on your way home." Her husband 's response astonishes her. "You think I've got nothing to do but run errands. I work during the day. If you didn't waste so much time on the phone, you'd have time to get the snowsuit yourself." Hurt by his attack, the wife tries a combination of logic and counterattack by saying, "It'll only take you 10 minutes. If you worked half as hard as I do, you'd find out what busy is. You'd probably earn a lot more money too!"