Do you normally include the ʻoe in imperatives or does it work to say just e + verb as well?
My sense is you would include it if there is an object, but I'll leave confirmation of that to the native speakers.
Including "ʻoe" is usually not necessary, especially since you'd be speaking to that person, so they would know you were talking to them. An object is obvious by the use of "i" before it, which is a directional marker, so in this sentence "[You] Clean the kitchen" the cleaning action is done to the kitchen.
I asked about the word "e" in the context of "let's", and it is appearing again here. What does it actually mean? What is its use in the sentence? Mahalo!
"E" can be used either before a name or pronoun to show who you're speaking to, or before a verb to make it imperative (i.e., a command or an expected action like GeraldMath4 said)