Pierre and others have covered how to get SNPs from OMIM genes: Disease Associated Snps

The table you can download with these direct links is here

You can find more here about Finding Records with OMIM Data/Links: http://www.ncbi.nlm.nih.gov/books/NBK44379/#Search.Finding_Records_with_OMIM_DataLin

What dbSNP report format will provide both a SNP and its specific OMIM ID number?

The easiest way you can get all the SNPs with OMIM links is from Entrez SNP:

1. Go to the Entrez SNP site.
2. Click on the grey “Limits” tab near the top of the page (just beneath the text search boxes).
3. Select the organism you are interested in from the organism list located at the top left of the page.
4. Scroll down the page almost to the bottom, until you find the list of “Annotation” limits. Select “OMIM”
5. Press the “Go” button located at the top of the page next to the empty text search box, and you will receive a list of your organism’s SNPs with OMIM annotation.

You can also get those SNPs with an OMIM ID number by downloading from the dbSNP FTP site: the OmimVarLocusIdSNP table contains the information you need for your organisim of interest (human, in this case). This table is located in your organism’s organism_data directory on the dbSNP FTP site.FTP site.

I don't understand your problem and what you're trying to do with Efetch.

The command should be NCBI ELINK. Something like:

 curl "http://eutils.ncbi.nlm.nih.gov/entrez/eutils/elink.fcgi?dbfrom=snp&id=121965089&db=omim"


http://www.ncbi.nlm.nih.gov/entrez/query/DTD/eLink_101123.dtd">
<eLinkResult>

        <LinkSet>
                <DbFrom>snp</DbFrom>
                <IdList>
                        <Id>121965089</Id>
                </IdList>
                <LinkSetDb>
                        <DbTo>omim</DbTo>
                        <LinkName>snp_omim</LinkName>
                        <Link>
                                <Id>300614</Id>
                        </Link>
                </LinkSetDb>
        </LinkSet>
</eLinkResult>

ClinVar data dumps can also be used to link dbSNP identifiers to Omim Id.

For more info on ClinVar data files - https://www.ncbi.nlm.nih.gov/clinvar/docs/maintenance_use/

Mapping for ClinVar VCF data file is quite straightforward. The ID column corresponds to the dbSNP ID. The OMIM ID has to be extracted from the INFO column. Look for CLNSRC="OMIM" or "OMIM_Allelic_Variant", then use the corresponding value in CLNSRCID to get the OMIM ID or OMIM allelic variant ID.