Very mild adjective, roughly the same obscenity level as "darned" or "bloody". For some obscure reason, Americans (who use the word "sodding" to mean putting turf (or sod) down in your garden) have got the impression that it is of about the same obscenity level as "f***ing" whereas it is not uncommon to hear your elderly aunt, who wouldn't dream of saying "shit", use it.
Blimey, it's sodding cold today - or - has anyone seen my sodding keys?
Teacher: OK class, get out your homework!
Student 1: What homework?
Student 2: You know, the maths worksheet.
Student 1: Oh yeah. the sodding maths worksheet.