I'm just starting my first D&D 5e campaign, playing as a Kenku rogue. The DM is giving me a lot of leeway, but I'm rather enjoying using only mimicked phrases and actions to communicate. As the campaign progresses I'm sure I'll have need of more intricate phrases to communicate thoughts and dangers to the party. I also expect I'll need to keep a running catalogue of words, sounds, and phrases (with associated character/NPC/monster) to draw on when needed.
Communicating as a Kenku is very different than other races, and I'm enjoying the race even with these limitations, but it looks like communication will get harder as dungeons get more complex. I've currently been doing things like answering questions with portions of the questions asked and used the sound of a church bell to ring out a warning.
How can I best portray a Kenku at the table in terms of both communicating and in keeping track of known words, phrases, and sounds?