No he generally cannot claim Head of Household with a 21 year old. Your son is no longer a qualifying child unless he is enrolled in school, or permanently disabled.
Since it is a "qualifying relative," if he does qualify as such, only the exemption can be claimed. Head of Household, the EIC, Child Tax Credit, and other things associated with a "qualifying child" no longer apply unless he is enrolled in school or disabled.
If 1) you guys have another child under the age of 18 that lived with one of you, or your child was in school, and 2) you did not live together for the last six months of the year, you can claim Head of Household under an exception. Otherwise you must file as Married Filing Jointly or Seperately because you were married on the last day of the year, and you are not legally seperated.
I agree with attorney Larson. This is a very complex set of facts and it would be a good idea for you to retain a CPA to prepare your returns to make sure you follow the law correctly.
Any individual seeking legal advice for their own situation should retain their own legal counsel as this response provides information that is general in nature and not specific to any person's unique situation. Circular 230 Disclaimer - Advice given in this response cannot be used to eliminate penalties with the IRS or any other governmental agency.