For the multihit jabs, DI down and try to immediately roll out (behind if they're multihit jab) and punish. For single jabs and frame traps, try to smash DI down and roll out as well. Against Luigi, choose the option that leads to him not getting a grab, preferably.
If you land an aerial, you don't NEED to follow up. This isn't melee, getting single hits in neutral is fine. If you space a back air and knock them away, use it to get into a good position outside of their options, or get a banana out, or set a frame trap with monkey flip. If you get a knock down, one thing you can do is run up and Shield to cover get up attack and spot get up, and monkey flip to punish rolls if you're fast enough.
If they are aerialing your shield, upsmash out of shield is great, and has great range IN FRONT of Diddy. But you also have the single best option out of shield as Diddy. Keep a Banana in hand. Banana lets you instantly punish any aerial regardless of how well they space it. Banana negates any shield pressure and makes it a huge risk for them to do. Just holding a banana changes so much in how matchups play, and it is by and far one of the main reasons Diddy is amazing.
tl;dr bananas and spacing.