The difficult with marrying here is that you would have to apply for a certificate of approval for marriage:-
Although you do not have status in this country at present, this does not prevent the UKBA from issuing a certificate of approval they would no doubt drag their heels over it. They could deport you in the meantime, which is the risk.
Alternatively if you are both over 21 years of age you can marry in an Anglican Church here without having obtained a COA. Again, though there is the risk that you are deported in the meantime.
If you could get a visa to travel to Belgium you could marry there.
The safest way would be to return to Nigeria and marry your partner there.
Once you are married and intending on both returning to the UK to reside then you will have to apply for apply for a residence card due to your marriage to an EEA national. This would allow you to stay in the UK with your husband. Here is the link to the UKBA's page on an application on this basis:-
The overstay will not in and of itself be fatal to your application because you can argue your Article 8 Right to Family and Private Life under the Human Rights Act, this should supersede the overstay provided there are no other defects with your application.
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