Ils viennent voir toi et moi.

Stress pronouns DO have an English equivalent....sort of. As in:

"Hey, you!" -- "Who, me?" and not "Who, I?"

Yes, you are correct. That's as close as you can come to a stress pronoun in English.

My brother and me -- Mon frère et moi.
My brother and I (sounds a bit stilted) -- Mon frère and je (plain wrong).

-- Chris (not a native speaker).

Eh... I only rarely hear constructions like "Doug and me played cards." Not even informally, among friends, or when messaging. It would be considered an error to us. Maybe it's regional.

But "John and I were friends" is never wrong and doesn't sound the least bit stilted to me!

“Hugo and they” is grammatically correct English (technically) but you and pretty much everyone else would say “Hugo and them”   

Hi John,

Indeed, "John and me" is incorrect English, even though frequently heard in colloquial English. However, there does exist in English a kind of parallel to the French stress pronouns. Here is what I mean:

"Hey, you!" - "Who, me?" -- In this case "who, I" would be unnatural. In this case "I" is replaced by "me" which functions as a kind of stress pronoun for "I". This works for other persons as well:

I -- me
you -- you
he/she/it -- him/her/it
we -- us
you -- you
they -- them

It's curious, but in English the use of the stress pronouns also seems to depend on the position within the sentence:

"My brother and I are going out." -- correct.
"My brother and me are going out." -- incorrect.
"Me and my brother are going out." -- correct.
"I and my brother are going out." -- incorrect (or at least awkward).

So your question has more to do with English than with French.

-- Chris (not a native speaker).

Chris, you would NEVER say "Me and my brother are going out".  That is incorrect.  The only way to say this is "My brother and I are going out".  "I and my brother are going out" IS awkward but it's not incorrect.

He's American. Any English linguists in that host?   

My brother and I are subject pronoun(s), so when they are the subject, use I. My brother and me are object promoun(s). Use when they are the object.

 "My brother and I walked down the street." Or "My brother and me walked down the street." ? Knockout "my brother" and see how it sounds. "I walked down the street." Or "Me walked down the street." 

This is true in American English, as well. "Me" is an object pronoun, not a subject pronoun. "My brother and me" used as a subject is always incorrect, even if people commonly say it either by choice or by ignorance of the rule. 

Thank you Melisa.  I sometimes hear "me and him went to the  movie..."  Again, object pronouns, not subject!

Hi Shruti,

you need the stress pronoun "lui" here. Even in English you would say: "Marie and HIM" which is the English version of a stress pronoun. 

-- Chris (not a native speaker). 

Hi Shruti,

again, this is a case of stress pronouns. "Toi" is the stress pronoun for "tu" and "elle" is the same as personal and stress pronoun. 

-- Chris (not a native speaker).