A later due date wouldn't put them off
I've tried that this time round, and still am being asked if I've had the baby yet, or if I've had any twinges (childbirth does not involve fucking twinges) - I too am 38w.
You are not obliged to tell them anything (especially when you go into hospital, because then they'll probably want hourly cervix reports from your DH despite routine checks normally being every four hours, and if he can't tell them anything they might well try their luck with the main maternity unit line)
Whilst it is understandable that they are excited and anxious, it's no good them passing on their anxiety to you.
People might say to you 'oh, but they mean well' but when it's several times a day and it's not normal for them to contact you so frequently, there is no quicker way to make you stabby.
You need to get firm with them. Tell them, clearly, that you will call them when there is any news, and that whilst you know that they are excited and that they worry, the frequency of the calls is too much. Alternatively, record an answerphone message to say that there is no news, and that if anyone is calling for any reason other than to ask 'how you're doing, or if you've had the baby' then leave a message and you'll call back...at some point.