I live in a home with Joe. Joe has a lease with the home owner. I pay Joe a fixed amount of rent each month and he gave me keys when I moved in. We don't have a formal lease between us, but we do have a single email that specifies the expectations. It says nothing at all about moving out, vacating or terminating the agreement. What does this mean? In theory could he kick me out with only a days notice and if I refuse hire a bailiff to remove me and my belongings? Or can he basically not kick me out but I can choose to move out whenever I want?
There are credible arguments both ways.
If the email has merely granted you a "license" (which is the kind of right by which someone stays in a hotel, or a movie theater, or as a guest in someone else's house) it is revocable at will without due process or court proceeding.
If the email and the conduct of the parties amounted to a lease, a formal eviction would be necessary to remove you. In the absence of a more specific agreement between the parties, a lease of a residential property for personal use with an indefinite term under which payments of rent are made monthly is usually presumed to be a month to month lease, in which case the Residential Tenancy Act provisions related to notice of termination of month to month leases applies, although, since it appears to be a sublease, the RTA requirements are minimal.
The language of the parties, the communications of the parties with each other, and the course of dealings of the parties, and any other relevant context, would inform a fact finder's decision regarding whether or not there was a lease. If I were a lawyer advising Joe, I would tell him that it is unclear but that the safer and more conservative course of action would be to treat the relationship as a lease, even if it might actually have been a license under the law.
could he kick me out with only a days notice and if I refuse hire a bailiff to remove me and my belongings? Or can he basically not kick me out but I can choose to move out whenever I want?
This issue is quite unclear. Although the expectations email constitutes an express contract, your tenancy arrangement does not give an end date. Therefore it does not meet the statutory definition of sublease agreement given in the Residential Tenancy Act.
Furthermore, the Act contemplates subleases without barely formulating the sublease equivalent of "landlord" (which premised on ownership of the property, thereby discarding Joe). This is one legislative example of being very specific in some portions and sloppy on the rest.
The authorship and terms of the expectations email could be relevant in discerning whether the doctrine of contra proferentem readily solves your concern. Not knowing that, the most straight-forward approach seemingly consists of you proposing an amendment to the contract/email so as to address the issue of termination notice.