Similarly to Irisviel, if the scene features Illya's friends from school, it's going to be funny. That's just how they work.
Ruby and Sapphire decided to switch Masters because Rin and Luvia couldn't stop fighting. When they tried to include their respective Class Cards, the Kaleidosticks ended their contracts. Midair. A few hundred meters above the ground.
Illya is a big fan of anime and magical girls. That's why she is extremely Genre Savvy, even more so in the manga.
Illya's reaction when Ruby showed up to make her into a magical girl:
When Ruby concludes that they need to fly to hit Caster, Rin notes how difficult it is. However, Illya easily flies, because:
Illya: Don't all magical girls fly?
Ruby in general really loves teasing Illya and Rin. There are way too many scenes, but here's an example: In the last third of Episode 1, where the story proceeds to skewer various magical girl tropes, with poor Illya along for the ride while the mildly psychopathic Ruby takes the opportunity to take revenge on Rin. What really makes the whole thing perfect is the brilliant voice acting, never faltering in that sickeningly sweet tone:
Ruby: Very well. Illya-san, point me towards Rin-san while saying "damn you" in your head.
Illya: Um. (points Ruby at Rin) *half-hearted* Damn yoooouuu.
Rin: (Rin's getting electrocuted) AAAAAHHHHH!
Illya: (shocked) Whoa, it shot something!
Ruby: Fufu. Illya-san's answer is as follows: "I'm not giving this stick to anybody. Go back to where you came from, you twintailed hag!"
Illya: I didn't say that!
Rin: (starts shooting Gandr shots) WHAT WAS THAT FOR!? TAKE THIS!
There are so many Mythology Gags in this series. For instance, at the end of the first chapter, instead of Saber asking whether Shirou is her Master...
Rin: From now on, you will be my Servant!
Illya is getting really excited when she finds a letter addressed to her. Ruby immediately thinks it's a love letter and Illya is getting all flustered and blushes. When she opens the letter:
Rin: Tonight at midnight, come to the highest point in the schoolyard. If you don't show up, I'll (striked-through) kill you come for you.
[cut to Illya and Ruby showing very disappointed faces]
Ruby: Shall we go home, Illya-san?
Rin's "love letter" is a reference to the Heaven's Feel route, where Shirou receives a very similar letter from Rin. Note While that particular scene is pretty funny, it will lead to a Bad End.
In episode two, Ruby tries to teach Illya how to use a magical girl's strongest weapon. Illya is supposed to do a twirl, place her fingers on her cheeks and give a nice smile. When she tries it a few times and still doesn't see any weapon:
Ruby: Very cute indeed.
Illya: You are just making fun of me! Ruby, you are definitely making fun of me!
Ruby: What are you talking about? A magical girl's number one weapon is her cuteness!
Illya: I've never heard of something like that!
Speaking of embarassing things, Illya does her transformation in a restroom because it happens in real-time, with all the music and light effects, and she finds it extremely embarassing.
Illya has no idea how to fight the Rider card. So when Ruby tells her to make some distance, she immediately runs away.
Miyu is way too intelligent for an Elementary School student to the shock of everyone, including Taiga. Miyu's confused look when told there was no need to solve for the volume of a cone with an integral is priceless.
And when she does weak up, she's extremely bored because she has a fever and can't do anything besides sleeping.
The first scene that usually comes to mind is Illya utterly freaking out over Miyu's maid uniform. When Illya sees Miyu in her uniform, she talks about a strange switch in a similar way she narrated her fight against Saber Alter, and ends up mounting Miyu while wearing an expression◊ that would be more appropriate on a psychotic thrill-killer than a girl who thinks maids are cute. Poor Miyu...
Ruby even scolds Illya for overdoing it and tells Illya to apologize:
Illya: Please forgive me. It's the fault of that strange switch.
Ruby: Haa, haa... You didn't play along, Sapphire-chan. Nee-chan is lonely...
Sapphire: No need for dumb games, Nee-san.
Illya almost killed everyone when she nuked Assassin. How does she react when she remembers this and how she defeated the previous card? She teleports away and leaves everyone else dumbfounded.
Illya is very depressed after Rin relieved her from her magical girl duties. Then her mother Iri shows up out of nowhere and wants to take a bath with Illya "to improve [their] mother-daughter relationship".
Iri acts very serious when she reveals things about Illya's hidden power. When Illya asks for more details:
Illya: Mama... you knew? About my power? Then tell me! What is that power? What do I-
Tatsuko: Damn you, Illya! You unlocked the Miyu route that we wanted to get!
Luvia manages to steal Rin's Class Cards and flees on a helicopter to get all the credit and become Zelretch's pupil. What does Rin do? She brings down the helicopter and lets Luvia kiss the ground. And then she is told that both her and Luvia need to learn some manners and stay in Japan for another year. Cue enraged Rin destroying her phone.
Illya recognizing just a second too late that 'I thought you were my brother' is really not the best excuse for why you just surprise-French-kissed someone.
Rin and Luvia bickering and complaining throughout the entirety of Illya and Miyu's transformation.
Iri pulls off a giant fist made out of strings to silence Kuro after Kuro almost attacked Iri. Then she proceeds to do the same with Illya just because. Kuro is seen with two bumps because she shares Illya's pain.
Illya's friends again. Highlights in this season include:
Calming Tatsuko down by putting a bag over her head as though she were a scared horse... and it works.
The net result of their attempts to 'make Illya into an elegant big sister'.
Chapter 12 of Zwei. The cooking duel chapter. The whole damn chapter, barring maybe six or so pages. Particularly any moment Tatsuko is on-panel.
Kuro stealing the Sacred First Kiss of all of Illya's friends, causing all of them to pile up on the rooftop and demanding compensation. Of all people, Taiga is also among them and looks the most depressed.
You kissing demon!
Later, Tatsuko complains again, namely because she wanted to have her Sacred First Kiss with her older brother (though it's not clear which of thw two). She gets immediatly compared to Illya, who is not happy about that.
Chapter 5 has Miyu's defence wall made of brooms rammed into the ground.
Particularly the revelation that cute, innocent lil' Mimi has become a complete and utter pervert. "And then they *** with their *** and they did the ***!"
And not only that, but the example picture when Kuro's explaining the boy's love genre is a silhouette of Kirei and Kiritsugu. There are no words.
After Suzuka's elder sister explains that they know Boy's Love is a fantasy and will eventually settle down with a boyfriend, Mimi says she isn't planning on it. When told she's a little young to settle for forever alone, she explains:
Mimi: I just think boys should love boys and girls should love girls!