How do I list installed packages with source URI, distribution and section in Debian?

As well as apt-cache policy, described in Braiam's answer, you can use apt-show-versions and apt-forktracer.

apt-show-versions by default will list all installed packages with the suite they come from, their version and whether they can be upgraded; for example

afl:amd64/experimental *manually* upgradeable from 1.28b-1 to 1.36b-1
agedu:amd64/testing 9723-1 uptodate
devio:armhf 1.2-1 installed: No available version in archive

With the -a option it lists the installed version and all available versions in all the repositories you have configured:

afl:amd64 1.28b-1 install ok installed
No stable version
No testing version
No unstable version
afl:amd64 1.36b-1 experimental ftp.fr.debian.org
afl:amd64/experimental *manually* upgradeable from 1.28b-1 to 1.36b-1
agedu:amd64 9723-1 install ok installed
No stable version
agedu:amd64 9723-1 testing  ftp.fr.debian.org
agedu:amd64 9723-1 unstable ftp.fr.debian.org
No experimental version
agedu:amd64/testing 9723-1 uptodate

apt-forktracer lists the packages which don't come from the standard repositories or whose installed version doesn't match those available in the standard repositories:

afl (1.28b-1) [Debian: 1.36b-1]
bb (1.3rc1-8.2) [Debian: 1.3rc1-8.1+b1 1.3rc1-8.1+b1]
biew (5.7.3.1-0.1) [SK2: 5.7.3.1-0.1]

-l is one of the options of dpkg-query, which has another option, -W (or --show). -W allows use to select an output format. You can try:

dpkg-query --showformat '${Status}\t${Package}\t${Version}\t${Architecture}\t${Origin}\t${Section}\n' -W | 
  column -ts $'\t'

For example:

$ dpkg-query --showformat '${db:Status-Abbrev}\t${Package}\t${Version}\t${Architecture}\t${Origin}\t${Section}\n' -W | column -ts $'\t' | head
ii  account-plugin-aim           3.8.6-0ubuntu9.1                amd64  gnome
ii  account-plugin-facebook      0.11+14.04.20140409.1-0ubuntu1  all    gnome
ii  account-plugin-flickr        0.11+14.04.20140409.1-0ubuntu1  all    gnome
ii  account-plugin-google        0.11+14.04.20140409.1-0ubuntu1  all    gnome
ii  account-plugin-jabber        3.8.6-0ubuntu9.1                amd64  gnome
ii  account-plugin-salut         3.8.6-0ubuntu9.1                amd64  gnome
ii  account-plugin-twitter       0.11+14.04.20140409.1-0ubuntu1  all    gnome
ii  account-plugin-windows-live  0.11+14.04.20140409.1-0ubuntu1  all    gnome
ii  account-plugin-yahoo         3.8.6-0ubuntu9.1                amd64  gnome
ii  accountsservice              0.6.35-0ubuntu7.1               amd64  admin

The URI is not known to dpkg, since that's a frontend (apt) concern. It shouldn't be that difficult to use awk or something to obtain it too, though.

You are looking for apt-cache policy output:

➜  ~  apt-cache policy skype
skype:i386:
  Installed: 4.3.0.37-1
  Candidate: 4.3.0.37-1
  Version table:
 *** 4.3.0.37-1 0
        100 /var/lib/dpkg/status
➜  ~  apt-cache policy irssi
irssi:
  Installed: 0.8.17-1
  Candidate: 0.8.17-1
  Version table:
 *** 0.8.17-1 0
        900 http://http.debian.net/debian/ testing/main amd64 Packages
        500 http://http.debian.net/debian/ unstable/main amd64 Packages
        100 /var/lib/dpkg/status
➜  ~  apt-cache policy megasync
megasync:
  Installed: 1.0.39
  Candidate: 1.0.39
  Version table:
 *** 1.0.39 0
        500 http://mega.nz/linux/MEGAsync/Debian_7.0/ ./ Packages
        100 /var/lib/dpkg/status

In this case, the installed version of skype isn't available from any repository (that includes local installation), irssi is installed from Debian repositories, and megasync is from a third party repository.