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If the 70-300 is the CANON Objectif EF 70-300mm f/4-5.6 is II USM, it has a 67mm filter thread and would fit. It does not fit the 18-55 because this lens has a smaller diameter. Filter adapter rings are required to use the filters on it. These are available from around €12. 

Better is the sigma adapter...don't hesitate 

The adapter is designed for Nikon lenses, including D mount. If the Tamron fits the Nikon D80 it should work. As for the lack of aperture ring on the Tamron ... not sure about that. Perhaps the Nikon D80 has an in camera aperture selection. 

The adapter will mount the lens and you will be able to use it manually. However, my copy of the adapter does not allow the lens to be fully mounted all the way until it clicks into place. It doesn't quite make it, but it's still very solidly mounted. Also, the manual aperture linkage doesn't work properly (on my copy, at least) so exposure is controlled only by shutter speed and/or ISO. You will be able to manually focus and zoom the lens but no VR, of course. It will be a frustrating experience. Instead, get a 14-140 Panasonic zoom if you can afford it!