This annoying issue occurs because libgdal was forked between libgdal1 and libgdal1h last year. Ubuntu GIS stable uses libgdal or libgdal1, Ubuntugis unstable uses libgdal1h.
GDAL is a translator library for raster geospatial data formats.
As a library, it presents a single abstract data model to the
calling application for all supported formats. The related OGR
library (which lives within the GDAL source tree) provides
a similar capability for simple features vector data.
You will have to start from fresh.
Make sure you uninstall all software remnants of Ubuntugis Stable / Unstable. Uninstalling libgdal, libgdal1, libgdal1h will remove all software that depends on it. Then check your repos, make sure Ubuntugis Stable & Unstable isn't there.
Then add these repos for QGIS 2.2, Saga 2.1 and Postgres 9.3.3 & PostGIS 2.1.1.
http://www.qgis.org/en/site/forusers/alldownloads.html#ubuntu
Johan Van de Wauw's saga-gis repository
https://wiki.postgresql.org/wiki/Apt
I usually install QGIS first then SAGA, Grass, PostgreSQL 9.3.3, PostGIS 2.1.1, postgresql-contrib-9.3 and finally pgAdmin3.
There are a few small issues. This will install Grass 6.4.3-2, which might not work from Processing in QGIS 2.2. Grass 6.4.3-3, provided by Ubuntugis Unstable, is supposed to fix the problem (but did not work for me on Ubuntu 13.10).
Also, only Ubuntu GIS Unstable provides pgRouting as far as I know (with PostgreSQL 9.1 & PostGIS 2.1.0). If you want pgRouting you will have to compile it from source, it only takes few minutes. If Configure complain that Postgresql-9.1 is not installed, install postgresql-server-dev-9.1 and try again.
I had faced a similar problem installing qgis. I finally got it installed using aptitude package manager.
Try this first:
sudo apt-get update then sudo apt-get -f install.
If that doesn't work try the higher level package manager aptitude.
sudo aptitude install qgis python-qgis qgis-plugin-grass
It gives multiple solutions like this and you can select one.
Accept this solution? [Y/n/q/?] n
The following actions will resolve these dependencies:
Downgrade the following packages:
1) libqt4-declarative [4:4.8.7+dfsg-7ubuntu1~xenialoverlay1~1 (now) -> 4:4.8.7+dfsg-5ubuntu2 (xenial)]
2) libqt4-network [4:4.8.7+dfsg-7ubuntu1~xenialoverlay1~1 (now) -> 4:4.8.7+dfsg-5ubuntu2 (xenial)]
3) libqt4-opengl [4:4.8.7+dfsg-7ubuntu1~xenialoverlay1~1 (now) -> 4:4.8.7+dfsg-5ubuntu2 (xenial)]
4) libqt4-script [4:4.8.7+dfsg-7ubuntu1~xenialoverlay1~1 (now) -> 4:4.8.7+dfsg-5ubuntu2 (xenial)]
5) libqt4-sql [4:4.8.7+dfsg-7ubuntu1~xenialoverlay1~1 (now) -> 4:4.8.7+dfsg-5ubuntu2 (xenial)]
6) libqt4-sql-sqlite [4:4.8.7+dfsg-7ubuntu1~xenialoverlay1~1 (now) -> 4:4.8.7+dfsg-5ubuntu2 (xenial)]
7) libqt4-svg [4:4.8.7+dfsg-7ubuntu1~xenialoverlay1~1 (now) -> 4:4.8.7+dfsg-5ubuntu2 (xenial)]
8) libqt4-xml [4:4.8.7+dfsg-7ubuntu1~xenialoverlay1~1 (now) -> 4:4.8.7+dfsg-5ubuntu2 (xenial)]
9) libqt4-xmlpatterns [4:4.8.7+dfsg-7ubuntu1~xenialoverlay1~1 (now) -> 4:4.8.7+dfsg-5ubuntu2 (xenial)]
10) libqtcore4 [4:4.8.7+dfsg-7ubuntu1~xenialoverlay1~1 (now) -> 4:4.8.7+dfsg-5ubuntu2 (xenial)]
11) libqtdbus4 [4:4.8.7+dfsg-7ubuntu1~xenialoverlay1~1 (now) -> 4:4.8.7+dfsg-5ubuntu2 (xenial)]
12) libqtgui4 [4:4.8.7+dfsg-7ubuntu1~xenialoverlay1~1 (now) -> 4:4.8.7+dfsg-5ubuntu2 (xenial)]
Accept this solution? [Y/n/q/?] y
The following packages will be DOWNGRADED:
libqt4-declarative libqt4-network libqt4-opengl libqt4-script libqt4-sql libqt4-sql-sqlite libqt4-svg libqt4-xml libqt4-xmlpatterns libqtcore4 libqtdbus4 libqtgui4
The following NEW packages will be installed:
libdrm-dev{a} libfcgi0ldbl{a} libgl1-mesa-dev{a} libglade2-0{a} libglu1-mesa-dev{a} libjs-jquery-ui{a} libjs-leaflet{a} liblwgeom-dev{a} libqca2{a} libqca2-plugin-ossl{a} libqca2-plugins{a}
libqgis-analysis2.18.3{a} libqgis-app2.18.3{a} libqgis-core2.18.3{a} libqgis-customwidgets{a} libqgis-gui2.18.3{a} libqgis-networkanalysis2.18.3{a} libqgis-server2.18.3{a} libqgisgrass7-2.18.3{a}
libqgispython2.18.3{a} libqjson0{a} libqt4-dbus{a} libqt4-designer{a} libqt4-dev{a} libqt4-dev-bin{a} libqt4-help{a} libqt4-opengl-dev{a} libqt4-qt3support{a} libqt4-scripttools{a} libqt4-test{a}
libqtassistantclient4{a} libqwt5-qt4{a} libspatialindex4v5{a} libx11-xcb-dev{a} libxcb-dri2-0-dev{a} libxcb-dri3-dev{a} libxcb-glx0-dev{a} libxcb-present-dev{a} libxcb-randr0-dev{a} libxcb-render0-dev{a}
libxcb-shape0-dev{a} libxcb-sync-dev{a} libxcb-xfixes0-dev{a} libxdamage-dev{a} libxext-dev{a} libxfixes-dev{a} libxshmfence-dev{a} libxxf86vm-dev{a} mesa-common-dev{a} python-cycler{a} python-dateutil{a}
python-future{a} python-gdal{a} python-glade2{a} python-httplib2{a} python-jinja2{a} python-markupsafe{a} python-matplotlib{a} python-matplotlib-data{a} python-pygments{a} python-pyparsing{a}
python-pyspatialite{a} python-qgis python-qgis-common{a} python-qscintilla2{a} python-qt4{a} python-qt4-sql{a} python-shapely{a} python-sip{a} python-tz{a} python-yaml{a} qdbus{a} qgis qgis-common{a}
qgis-plugin-grass qgis-plugin-grass-common{a} qgis-provider-grass{a} qgis-providers{a} qgis-providers-common{a} qt4-designer{a} qt4-linguist-tools{a} qt4-qmake{a} x11proto-damage-dev{a}
x11proto-dri2-dev{a} x11proto-fixes-dev{a} x11proto-gl-dev{a} x11proto-xext-dev{a} x11proto-xf86vidmode-dev{a}
The following packages are RECOMMENDED but will NOT be installed:
qt-at-spi
0 packages upgraded, 88 newly installed, 12 downgraded, 0 to remove and 57 not upgraded.
Best Answer
If you stick to the ubuntugis-unstable ppa (with nothing from qgis.org in your sources list), you should be able to install QGIS 3.4.6 solely from the ppa.
BTW QGIS 3.4.4 is not the latest QGIS-ltr version; I wonder where you have that from. Maybe you should run
apt-cache policy qgisto see what is available for you.