This page explains in detail the interactions between the Mega Man series and the Strider series.
The Official Guide to Mega Man
1991
Mega Man
Strider
The Official Guide to Mega Man is a book licensed by Capcom USA which details the history behind the first three games in the classic Mega Man series. As this book was created very early in the franchise's story and by an English team, its completely different from the Japanese series canon and features story bits, characters and situations that are exclusive to it.
In the section dedicated to Mega Man 3, Mega Man's newly-introduced Slide move is described as a "Strider-style move" in direct reference to Strider Hiryu, who has a Slide maneuver in all his appearances.
Rockman 7
Strider's attack compared to the Slash Claw
March 24, 1995
Mega Man
Strider
In both Rockman 7 and its English version Mega Man 7, after beating a Robot Master and winning a stage, Mega Man transports to Dr. Light's lab and gets a brief description of his new weapon from the doctor. In the Japanese version, however, there's a random chance either Roll or Auto will appear instead of Light, providing more humorous commentary about the weapon in question. Auto's dialogue about the Slash Claw makes a direct reference to Strider Hiryu: Mega Man comments on how he can cut through anything with the Slash Claw, and Auto remarks that it's like "StrXdXr HiXyu", censoring the name possibly as a nod to the character's dual ownership between Capcom and Moto Kikaku.
The Slash Claw is also visibly similar to Hiryu's basic attack, generating an arc of energy in front of Mega Man when used just like Hiryu's Cypher creates an arc of plasma in front of him. The way Mega Man swings his arm to produce the attack also mimics Hiryu's movement when swinging his sword.
Mega Man Legends
December 18, 1997
Mega Man
Strider
Concept art for Mega Man Legends reveals a Strider Hiryu-themed armor was designed for MegaMan Volnutt to wear, but ended up being cut for unknown reasons. The armor is designed after Hiryu's standard uniform, with Volnutt wearing the iconic scarf as well. He has a weapon named the "Cypher Arm" based on Hiryu's Cypher sword, and Volnutt's little helper Data appears floating upside-down, mimicking the Option A assist robot from the first game.
Strider
A Light Capsule
February 18, 2014
Mega Man
Strider
There's a Mega Man easter egg featured in the 2014 Strider, located in the Research Facility area. In a secret room deep within the "Cloning Chamber" section of the facility the player can find a broken Light Capsule, the armor-granting capsules from the Mega Man X series, in the background. Upon entering Professor Schlange will insist Hiryu to leave the area, stating that there's "nothing to see there".
According to the game's director, the capsule was initially intended to hold the original Mega Man as a planned unlockable character. Unfortunately, a Capcom producer would eventually request the team to remove Mega Man from the game, and thus he decided to leave the broken capsule as a simple visual easter egg.