We can find Data Storage and File Storage using Salesforce Apex.

Option 1:

System.OrgLimit can be used to find Data and File Storage in MB.

Sample Code:

 Map < String, System.OrgLimit > limitsMap = OrgLimits.getMap();  
System.OrgLimit dataStorageLimit = limitsMap.get( 
    'DataStorageMB' 
);  
System.debug( 
    'Limit Name: ' + 
    dataStorageLimit.getName() 
);  
System.debug( 
    'Usage Value: ' + 
    dataStorageLimit.getValue() 
);  
System.debug( 
    'Maximum Limit: ' + 
    dataStorageLimit.getLimit() 
);  
System.OrgLimit fileStorageLimit = limitsMap.get( 
    'FileStorageMB' 
);  
System.debug( 
    'Limit Name: ' + 
    fileStorageLimit.getName() );  
System.debug( 
    'Usage Value: ' + 
    fileStorageLimit.getValue() 
);  
System.debug( 
    'Maximum Limit: ' + 
    fileStorageLimit.getLimit() 
);  

Option 2:

PageReference objPageRef = new PageReference(
    '/setup/org/orgstorageusage.jsp?id=' +
    UserInfo.getOrganizationId() +
    '&setupid=CompanyResourceDisk'
);
String strCompanyInfo = objPageRef.getContent().toString();
String strDataStorage = strCompanyInfo.substringBetween(
    'Data Storage',
    '</td></tr>'
).replaceAll(
    '&nbsp;',
    ' '
);
String strDataStoragePercent = strDataStorage.substring(
    strDataStorage.lastIndexOf( '>' ) + 1
);
System.debug(
    'Data Usage % is ' +
    strDataStoragePercent
);   
String strFileStorage = strCompanyInfo.substringBetween(
    'File Storage',
    '</td></tr>'
).replaceAll(
    '&nbsp;',
    ' '
);
String strFileStoragePercent = strFileStorage.substring(
    strFileStorage.lastIndexOf( '>' ) + 1
);
System.debug(
    'File Usage % is ' +
    strFileStoragePercent
);     

Use the above options to check the Data Storage and File Storage using Salesforce Apex.