We present maps and spectra of the HCN(1−0) and HCO+(1−0) lines in the extreme outer Galaxy, at galactocentric radii between 14 and 22 kpc, with the 13.7 m Delingha telescope. The nine molecular clouds were selected from a CO/13CO survey of the outer quadrants. The goal is to better understand the structure of molecular clouds in these poorly studied subsolar metallicity regions and the relation with star formation. The lines are all narrow, less than 2 km s−1 at half power, enabling the detection of the HCN hyperfine structure in the stronger sources and allowing us to observationally test hyperfine collision rates. The hyperfine line ratios show that the HCN emission is optically thin with column densities estimated at N(HCN) ≈ 3 × 1012 cm−2. The HCO+ emission is approximately twice as strong as the HCN (taken as the sum of all components), in contrast with the inner Galaxy and nearby galaxies where they are similarly strong. For an abundance ratio χHCN/χHCO+ = 3, this requires a relatively low-density solution for the dense gas, with n(H2) ~ 103−104 cm−3. The 12CO/13CO line ratios are similar to solar neighborhood values, which are roughly 7.5, despite the low 13CO abundance expected at such large radii. The HCO+/CO and HCO+/13CO integrated intensity ratios are also standard at about 1/35 and one-fifth, respectively. The HCN is weak compared to the CO emission, with HCN/CO ~ 1 /70 even after summing all hyperfine components. In low-metallicity galaxies, the HCN deficit is attributed to a low [N/O] abundance ratio; however, in the outer disk clouds, it may also be due to a low-volume density. At the parsec scales observed here, the correlation between star formation, as traced by 24 μm emission as is standard in extragalactic work, and dense gas via the HCN or HCO+ emission is poor, perhaps due to the lack of dynamic range. We find that the lowest dense gas fractions are in the sources at high galactic latitude (b > 2°, h ≳ 300 pc above the plane), possibly due to lower pressure.