I don't think that you have complex verb phrases here. All I can see is a single verb phrase (V-O eat dinner). In English, you can attach different grammatical units to a verb to indicate, among other things, the time the action takes place (past/ present/ future ...), the mood (indicative, subjunctive ... ), the aspect (continuous, completed ...) and so on.
"Would have been eating" is not a string of 4 verbs, but rather, a single verb "eat". "-ing" tells me that it is a continuous action; "would have" indicates that the "eating" is actually not occurring, meaning they are not actually eating, but eating was their original plan. For some reason not expressed in this sentence, they changed their plan and are not eating. In English, all this complex meaning can be expressed using grammatical units such as "would have", "been -ing".
Chinese, however, expresses these ideas differently. Semantic units, rather than grammatical units, are employed. Hence the word "originally" used by Google Translate. Actually, I think Google is doing a pretty good job here. It is able to decipher the grammatical unit "would have" as implying a change in the original plan, and employs a semantic unit "本来" for the job.
Here's how I would translate the sentences, without knowing the context. In context, I might do it differently.
They would have been eating dinner.
他們本來應該在吃晚飯。
他們 they
本來 originally
應該 should
在 *indicates continuous action
吃 eat
晚飯 evening meal
They would have kept being able to eat dinner.
他們本來應該可以繼續吃晚飯。
他們 they
本來 originally
應該 should
可以 be able to
繼續 keep on, continue to
吃 eat
晚飯 evening meal
They would have not been eating dinner.
I would prefer "They would not have been eating dinner."
他們本來不應該在吃晚飯。
他們 they
本來 originally
不 not
應該 should
在 *indicates continuous action
吃 eat
晚飯 evening meal
They would have not been able to keep eating dinner.
I would prefer "They would not have been able to keep eating dinner."
他們本來不應該可以繼續吃晚飯。
他們 they
本來 originally
不 not
應該 should
可以 be able to
繼續 keep on, continue to
吃 eat
晚飯 evening meal
- Note that 在 has multiple meanings depending on context.