food, meal, eat, offer
饈 centers on food and the act of eating, especially in the context of offering or presenting a meal. The meanings 'food', 'meal', 'eat', and 'offer' all connect to the idea of prepared sustenance being given or consumed.
饈 combines the food radical 飠 with 羞, which likely contributes both sound and the idea of offering or presenting. The exact historical development is uncertain, but the structure suggests a phono-semantic compound related to food and offering.
The left side 飠 means food. The right side 羞 looks like a hand offering something (the top part resembles a hand over a vessel). Picture someone presenting a meal with both hands: 饈 is food offered or eaten.
For シュウ, imagine offering a shoe-shaped cake as a meal: shoe -> シュウ, and the food radical 飠 reminds you it's about eating.