Hi sæton on þæm fæstenne.
They remained in the fortress.
And in this sentence it takes the accusative:
Her Ælle com on Brytenland and his þry suna.
Here Ælle and his three sons came to Britain.
Of course, on is not always about spatial relationships, and then the case of the object becomes less predictable. When on expresses time, for example, it may take the dative or the accusative. When used of looking at something (on hine locode), it usually takes the accusative. Generally one can see the relationship between the spatial and the other sense.
Prepositions that work like on include binnan within, into, bufan above, upon, innan in, within, ofer over, on, and under under, beneath.