[amenhotep]

These are all just different constructions that are related to "try and" only by coincidence. The fact that a different construction looks similar to a grammatically incoherent one by coincidence doesn't make the incoherent one coherent.

[mikepurvis]

I disagree. GP is laying is laying out reasonable scenarios that are a few dropped/implied words away from the otherwise incoherent ones. For my part, this one is very grating to my ears:

"Try and tell the truth"

Since it clearly should be "try to tell the truth"

However this one, while similar in construction, doesn't actually sound nearly as bad:

"Try and finish the assignment"

It can be fixed the same way ("try to finish") but it also accept GP's form too, which would be "try (to work hard) and (see if you can) finish the assignment". As I say, for whatever reason this second example sounds much more reasonable to me— I think at least in part my brain is much more accepting of a word that feels dropped than one that's misused.

[csande17]

There's a more standard, general rule in English grammar that web searches tell me is called "delayed right constituent coordination". It lets you read sentences like "He washed and dried the clothes" as "He washed [the clothes] and dried the clothes." The same object gets applied to both verbs.

I suspect that's what you're applying to these sentences. "Try and finish the assignment" makes some sense under this rule if you read it as "Try [the assignment,] and finish the assignment" -- an "assignment" is a thing that makes sense to "try". ("He tried [sushi,] and liked sushi" works for the same reason.) But "Try [the truth,] and tell the truth" doesn't work -- it doesn't make sense to interpret "trying" the truth as some separate action you're taking before you "tell" it.

So probably you just don't have the article's special try-and "pseudo-coordination" rule in your dialect.

[mikepurvis]

This makes a lot of sense, and it definitely explains where other "try and" sentences work while "try and finish" doesn't at all.

[ricardobeat]

The try and in “try and tell the truth” is a different idiom from “[try] and [x]” as two separate actions. It can almost always be replaced with “try to”.

For example, in “let’s try and finish this” it does not mean trying then finishing, it is try to finish. The construction is more obvious in a phrase like “try and stop me”. This phrasing is very common in movies, it might just not be as popular in your area.

[oasisbob]

Those examples seem to differ significantly because they're using "try" as an imperative.