Sealing gap between exterior door threshold and wood floor
I would use Quad Sealant. 

Use painters tape to mask off the floor boards and the threshold and then apply Quad with a caulk gun, Just enough not to much. 

Then dip you finger in Denatured alcohol and gently smooth it out by running your finger along the bead a couple of times to remove excess and make smooth. 

Remove tape repeat with the moistened finger, carefully and lightly, just enough to smooth out the lines left from pealing the tape off. 

You will still have the seams between the boards but the main gap between threshold and boards will be sealed. You may try to force some quad into those seams, Tape them off first, the quad is difficult to clean off.