How long does denture pain last?

Till an adjustment. If the pain is from the denture rubbing on the gums or from an uneven bite, adjustments will ease the discomfort right away.
Assuming this. Is a recent denture needing adjustment - relief is usually significant upon adjustment of the denture in the area of irritation. Typically one or two adjustment appointments is all that's needed. Call your dentist to be seen. Hope this helps.
Varies. It depends upon the source of the pain--if extraction sites are involved, bone heals slowly, if a sore spot is caused by the denture rubbing, an adjustment can correct that in a couple of days.
Maybe Implants. Dentures move all around. If you can have 4-6 mini-implants, then the denture can snap onto these implants thereby keeping them from moving. Remember that not all patients are good candidates for implants. If yor are, then do it if you can afford the cost.
It depends: If this was an immediate denture, you may be in pain till the extraction sites have healed. If there is no extraction sites under the denture, your dentist should likely be able to make them comfortable for you. Please note that there are times, especially on the lower, when so much ridge atrophy has occured that there is no retention for the denture and implants may be your best option.
Have Them Adjusted. You should not just let sore spots linger. Go to your dentist to have them adjusted.