Vodafone, as ISP, has nothing to do with your mails, especially if you are not using a Vodafone mail account but any kind of third party service (like gmail, outlook.com or such). In this case, Vodafone cannot unblock any mails as there is no mail traffic going through any of the Vodafone systems - this would only be the case if you'd use the Vodafone mail address. So if you are using a 3rd party mail provider, you have to ask that provider to help you - but I doubt they'll unblock any kind of address, especially if the setup of the originating email server is misconfigured.
Anyhow - as you are not contractual partner of Vodafone, Vodafone cannot help you at all. Vodafone will only help their contractual parters - as long as it is related to contractually agreed upon services. And I am not completely sure if your landlord is even allowed to sub-lease his line to other parties - as this is not allowed for customer lines, especially not in a commercial manner (e.g. he charges you).
