The standard errors in the 2013 Nigeria DHS report were calculated using the region by urban/rural (V024 cross V025) as stratification variable, which is the case for most of the DHS surveys. However, the 2013 Nigeria DHS used a more detailed stratification which is sate cross urban/rural and the stratification is coded in V022, but attention must be paid when use V022 (for the 2013 Nigeria DHS) as it has one single-cluster stratum, the urban of AKWA IBOM state. You may need to collapse it with the rural stratum of the state because sampling error calculation will not allow single-cluster stratum. If you want to replicate the DHS results on standard errors, you need to use V024 cross V025 as stratification. But you can use V022 as stratification, this gives the exact stratification used in the sample selection and this may give you more accurate results for other analysis such as modeling.
By the way, if you just want to produce point estimation with confidence interval (CI), you would better use Proc Surveymeans instead of Proc Surveyfreq. Proc Surveymeans will give you the 95% CI in the output. However, note that your results may not exactly match the published results, since DHS uses mean minus/plus 2 times the estimated standard error as confidence limits. While the SAS output uses mean minus/plus t(d.f, 95%) as confidence limits. You can use "Class" statement to produce results for urban/rural and regions separately within the Proc Surveymeans statement, and use "Domain" to produce results based on other social-economic, education or age group variables. Hope this helps.

To produce state level results, you can use V022 (sate cross urban/rural) as stratification variable. In Proc Surveymeans, you can add "Domain SHSTATE". It should produce the indicator results on the state level with the SE and 95% CI. However, we do not recommend you produce state level estimates, since the survey sample was not designed for this purpose, especially for the main indicators. The enough sample size to produce a DHS indicator differs based on the indicator type. For the TFR and the mortality rates, at least 800 to 1000 households is required for producing reliable indicators (with acceptable precision).

Regarding the mortality rates, if you are able to replicate the rate itself, it would be easy to apply the Jackknife variance estimation by applying the formula given in the DHS report appendix B; you need to calculate a series of UMR each time by dropping one cluster, then apply the formula.