It took a while for the full effects of Crisis to hit every corner of the DCU; this wasn’t the tightly planned crossover event that we usually see today. It was so loose that moments from Crisis were showing up in other titles months after the event had ended.
Oh, and the two titles that were most drastically altered by Crisis were the last ones to acknowledge it.

All-Star Squadron 56, 58-60
The main reason the first 3 issues here are noteworthy is that they still feature Superman, Batman, and Wonder Woman as members of the All-Star Squadron. This only happened on the Earth 2 version of the team.
It’s really business as usual in the All-Star Squadron until issue #60 when Roy Thomas pulls a very nice, very smooth switch from the Earth-2 steam to the new, Earth-1 version.
How? He more or less just doesn’t acknowledge that anything has changed, even though it has. Here’s the team photo from the middle of this issue:

And here’s that same photo when it’s delivered to President Roosevelt at the end of the issue:

It’s kind of surprising how easy this switch was. Batman, Robin, Superman, Wonder Woman, and Aquaman had to be pulled from the team as the team was no in a unified DCU, which meant that any characters who fought during WWII would be in their 60s after Crisis.
But Crisis takes away and Crisis gives back, because the Freedom Fighters of Earth-X no longer had a home. Presto change-o and you’ve got the perfect group of characters to replace those big name characters.
There’s also something perfect about Superman being replaced in that photo with Uncle Sam.

DC Comics Presents 94-95
Issue #94 is described on the cover as a “post-Crisis blockbuster” that features Lady Quark, Harbinger, and Pariah. It’s not essential reading by any means, but the fact that it takes place after Crisis is a little strange given that the following issue takes place DURING Crisis.
An interesting note is that Superman is pondering Crisis during issue #95 (the only real reference do it). The editor’s box notes that this story takes place “during the Crisis of 1985,” which is kind of a weird way to mention it. I suppose it’s fewer letters. Maybe this was while the proposed “Crisis of the Soul” series was on the books.

Green Lantern 199-200
Issue 199 doesn’t connect to Crisis aside from the fact that it takes place before the series concludes. It’s issue 200 where the connections appear. First, John Stewart tells one of the Guardians (a former Guardian, but that’s irrelevant to us) about the Crisis, as if he somehow wouldn’t have known about it, even being a former Guardian.
It’s issue 200 with the “important” moment. Hal, who has been newly reinstated into the Green Lantern Corps (this explains why John was the GL in Crisis) runs into Barry Allen.
At this point, Crisis was over and Barry had died a heroic death. But he’s alive here, or at least somewhat, anyway. He’s solid, but he disappears after telling Hal not to forget him. Barry also mentions that Batman saw him turn to dust.
Is Barry real? After he fades away Hal sees other dead people, all in advance of an attack by the Triumvirate of Terror (which is an awesome team name) featuring Star Sapphire, Hector Hammond, and Guy Gardner (god bless illiteration). So he could psychic projection by Hammond.
But he knows things only Barry would have known, this could be the “last” appearance of Barry Allen.

Infinity, Inc 25, 27, 30
Issue #25 features the introduction of the new characters that were introduced in the pages of Crisis. It gets explained in the comic itself and referenced as “the Crisis,” although there aren’t any more significant details given.
This is a strange kind of in between issue, though, as we’ve seen with a lot of these aftermath books. Power Girl talks about Huntress and Robin dying and her losing her past, but as we’ll see in issue #27, the impact of Crisis hasn’t fully happened yet.
It gets stranger with issue #27 as the entire issue is built around the idea of creating parallels between the Infinity, Inc. characters and their parents — including Fury and her Earth-2 mom, Wonder Woman.
In fact, Fury knows that her mother has been killed (?), but Brainwave, Jr. erases those emotions, which is a pretty awful thing to do, but also doesn’t solve the problem of Fury knowing that her mom was Earth-2 Wonder Woman even though Earth-2 doesn’t exist anymore.
Eventually, Fury’s mother is changed to a new WWII character also called Fury, although the younger Fury is raised by Miss America.
Issue #30 is a follow-up story to the Last Days of the Justice Society of America book below and mostly features the Infinity, Inc. kids trying to make sense of both the loss of their parents and the new world order. It’s a bit meta in that you can easily insert the creative team for Infinity, Inc., trying to figure out how they’re supposed to function in a unified DCU.

Last Days of the Justice Society of America
The question of whether or not this had to be done is a valid one. The Justice Society could have just been, well, old. They could have retired and we’d all be content to follow the adventures of their children. But I suppose part of the reasoning behind Crisis was to establish that the DCU was no longer tethered to a specific point in time.
Sending the JSA to limbo meant that they never had to age.