macos - How to get real root permissions on OS X

I'm a noob with OSX (10.8.5) wanting to install homebrew on an Airbook.

Installing homebrew fails straight away because it can't mkdir /usr/local.
So I try with sudo - same problem.
Trying
sudo mkdir /usr/local
directly also fails of course.

My user 'mjb' has admin rights (well according to the Users/Groups GUI interface) but I can't figure out how to do anything useful !

As my 'admin' user mjb, typing id shows "uid=502(mjb) gid=20(staff) ...."
typing sudo id shows "uid=503(root) gid=1000 ...."

I've searched and all the solutions I see involve editing some file (root.plist) directly or using visudo ... and of course I don't have the permissions to do that !

I just want "real" sudo access so I can install stuff on the command-line (boot2docker).

Thanks for any suggestions

Update:

dscl . ls /Users provides a lot of output:

_amavisd
_appleevents
_appowner
_appserver
_ard
_assetcache
_atsserver
_avbdeviced
_calendar
_ces
_clamav
_coreaudiod
_cvmsroot
_cvs
_cyrus
_devdocs
_devicemgr
_dovecot
_dovenull
_dpaudio
_eppc
_ftp
_geod
_installassistant
_installer
_jabber
_kadmin_admin
_kadmin_changepw
_krb_anonymous
_krb_changepw
_krb_kadmin
_krb_kerberos
_krb_krbtgt
_krbtgt
_lda
_locationd
_lp
_mailman
_mcxalr
_mdnsresponder
_mysql
_netbios
_netstatistics
_networkd
_postfix
_postgres
_qtss
_sandbox
_screensaver
_scsd
_securityagent
_serialnumberd
_softwareupdate
_spotlight
_sshd
_svn
_taskgated
_teamsserver
_timezone
_tokend
_trustevaluationagent
_unknown
_update_sharing
_usbmuxd
_uucp
_warmd
_webauthserver
_windowserver
_www
daemon
mjb
nobody
Paulina
root

dscl . read /Users/root

AppleMetaNodeLocation: /Local/Default
GeneratedUID: FFFFEEEE-DDDD-CCCC-BBBB-AAAA00000000
NFSHomeDirectory: /Local/Users/root
Password: *
PasswordPolicyOptions: 
;


    failedLoginCount
    0
    failedLoginTimestamp
    2001-01-01T00:00:00Z
    lastLoginTimestamp
    2001-01-01T00:00:00Z
    passwordLastSetTime
    2015-06-09T18:48:49Z


PrimaryGroupID: 1000
RealName:
 Mike Bright
RecordName:
 root
 BUILTIN\Local System
RecordType: dsRecTypeStandard:Users
SMBSID: S-1-5-18
UniqueID: 503
UserShell: /bin/bash