Argument to EHLO in the absence of a domain name
Section 4.1.3 Address Literals of RFC 2821 says:
Sometimes a host is not known to the domain name system and communication (and, in particular, communication to report and repair the error) is blocked. To bypass this barrier a special literal form of the address is allowed as an alternative to a domain name. For IPv4 addresses, this form uses four small decimal integers separated by dots and enclosed by brackets such as [123.255.37.2], which indicates an (IPv4) Internet Address in sequence-of-octets form.
so a simple EHLO [123.255.37.2]
suffices (with the actual IP address of your SMTP server of course). Or it could be a properly formatted IPv6 instead.
Required headers
Section 3.6. Field definitions of RFC 2822 says:
The only required header fields are the origination date field and the originator address field(s). All other header fields are syntactically optional.
so only From:
and Date:
are required.