How to extract metadata from NCBI's experiment?

You'll want something like:

esearch -db sra -query SRX1596422 | efetch -format runinfo

This will produce a CSV output to the screen with columns containing the meta information available in SRA:

Run,ReleaseDate,LoadDate,spots,bases,spots_with_mates,avgLength,size_MB,AssemblyName,download_path,Experiment,LibraryName,LibraryStrategy,LibrarySelection,LibrarySource,LibraryLayout,InsertSize,InsertDev,Platform,Model,SRAStudy,BioProject,Study_Pubmed_id,ProjectID,Sample,BioSample,SampleType,TaxID,ScientificName,SampleName,g1k_pop_code,source,g1k_analysis_group,Subject_ID,Sex,Disease,Tumor,Affection_Status,Analyte_Type,Histological_Type,Body_Site,CenterName,Submission,dbgap_study_accession,Consent,RunHash,ReadHash
SRR3184375,2016-02-24 00:00:00,2016-02-23 23:14:45,556018223,111203644600,556018223,200,57997,GCA_000001635.1,https://sra-downloadb.be-md.ncbi.nlm.nih.gov/sos2/sra-pub-run-7/SRR3184375/SRR3184375.1,SRX1596422,,WGS,size fractionation,GENOMIC,PAIRED,0,0,ILLUMINA,Illumina HiSeq 2000,SRP070623,PRJNA312530,,312530,SRS1306521,SAMN04492320,simple,10090,Mus musculus,MCNT_E1,,,,,female,,no,,,,,THE SCRIPPS RESEARCH INSTITUTE,SRA356784,,public,52A6F836C13F2D15755EDE3E52A18D78,240E7130CFE36405818DA5EE2A10E24C

The more relevant fields are: Subject_ID, Sex, Disease, Tumor, Affection_Status, Analyte_Type, Histological_Type, Body_Site. Note that not all of these are available for that particular sample.