Does lightning:recordEditForm supports Task and Event object?

Your assumption seems to be right. Tried this in a quick app and could see that the error message returned specifies the object (Task or Event) not to be supported.

Below is the sample code and the error on UI.

Code:

<aura:application extends="force:slds" controller="TestBed">
<lightning:recordEditForm aura:id="editForm" objectApiName="Task" >
    <lightning:messages />
    <lightning:inputField aura:id="email" fieldName="Email" />
    <lightning:button class="slds-m-top_small" variant="brand" name="update" label="Update" onclick="{!c.onSubmit}"/>
</lightning:recordEditForm>

Error when the app loaded: