Do I use a plural or singular verb in this sentence? Is one more accurate than the other?
I think it should be plural-agreeing "have" (unlike others who have commented so far). Does the subject of the verb refer to more than one thing? If so, the plural-agreeing form should be used.
Then we need to decide whether "our work and others' work" is just one thing or two things. If our work and other's work referred to just one thing, as for example in some collaborative effort, it is that single work that would be referred to. I don't think that is a possible interpretation, here. Maybe it would be if if the reference was to "our and others' work" (as compared with "our and others' works").
I don't see the relevance of "work" being a mass noun. I say my work and your work "are the same", not "is the same" (though it's true I could say "our work is the same"). But what does that have to do with whether "work" is a mass noun? I could say to my wife that my son and her son is late, yet again, though "son" is not a mass noun.
In your example sentence you have no choice but to use the singular.
For the avoidance of doubt, the plurality or otherwise of 'has/have' has nothing to do with the adjacent 'others'. The verb follows the plurality of the subject, which is 'our work and that of others'. The question is: is that a singular or a plural noun phrase?
Not many speakers would argue that 'our work' + '[work] of others' adds up to two 'works'. Other than in the specialised usage of 'book', 'work' is a mass noun. It doesn't get pluralised. 'You do some work, I do some work; together we do some work' (as opposed to 'I write a work of literature, you write a work of literature, together we write some works of literature'). In the sense of 'work' as 'labour', the subject is singular and the verb should be 'has'.
If the sentence had instead been 'My subscription and that of my parents has/have expired', there would have been more room for debate. I would have gone for the plural, in that the subject is the total of two subscriptions. However, the singular doesn't sound terrible either, because you could rephrase the sentence as 'My subscription has expired, and so has that of my parents.'