You should be able to get to most places for less than $2500, even from Oslo. I really have nothing better to do right now and enjoy looking this shit up so here's some possible ideas.
Since you seem to have a pretty broad criteria, I just typed in "flights from oslo" in Google. Here is the abridged version of non-stop flights from Oslo:
To Duration Airlines
Agadir, Morocco 5h 5m Norwegian - Morocco isn't really a DP but you can head south into W. Sahara and Mauritania.
Antalya, Turkey 4h 20m Norwegian - skirt the coast and head to border area w/ Syria, crossing over if possible. rickshaw was just there and details are on the board. Cyprus is a flight/ferry ride away as is Lebanon.
Bangkok, Thailand 10h 50m Thai - You can get up to all sorts of trouble here. Other places an easy flight away.
Belgrade, Serbia 2h 50m Norwegian
Doha, Qatar 6h 25m Qatar
Dubai, United Arab Emirates 7h 0m Norwegian - good transit point for other places in Africa, ME, S Asia
Geneva, Switzerland 2h 35m Norwegian - die from boredom
Islamabad, Pakistan 7h 0m Pakistan
Istanbul, Turkey 3h 40m Turkish
Moscow, Russia 2h 22m Aeroflot, SAS - go around the time of the elections (March)
And since that really didn't reveal much here's some ideas
from Dubai (Oslo - Dubai on Norwegian is a little over 500 euros r/t; 371 euro on Lufthansa via Munich):
To Duration Airlines
Accra, Ghana 9h 0m Emirates
Addis Ababa, Ethiopia 4h 5m Ethiopian, Emirates, flydubai
Aden, Yemen 3h 0m Yemenia
Al Basrah, Iraq 2h 0m Emirates
Aleppo, Syria 3h 55m flydubai
Alexandria, Egypt 4h 17m flydubai, EgyptAir
Algiers, Algeria 7h 30m Air Algerie
Ashgabat, Turkmenistan 2h 27m flydubai, Turkmenistan
Baghdad, Iraq 2h 47m Emirates
Baku, Azerbaijan 2h 57m Azerbaijan, flydubai
Beijing, China 7h 43m Emirates, Air China, China Southern, …
Beirut, Lebanon 3h 43m flydubai, MEA, Emirates
Berbera, Somalia 3h 15m Jubba Airways, African Express
Bishkek, Kyrgyzstan 4h 2m Altyn Air, Air Bishkek
Cairo, Egypt 4h 8m EgyptAir, Emirates, Singapore Airlines
Dakar, Senegal 10h 55m Emirates
Dar es Salaam, Tanzania 5h 30m Emirates
Dera Ghāzi Khān, Pakistan 2h 45m Pakistan
Dhaka, Bangladesh 4h 33m Emirates, flydubai, GMG, …
Dimashq, Syria 3h 25m Emirates, flydubai, Syrian Air
Djibouti 3h 25m flydubai
Durban, South Africa 8h 45m Emirates
Dushanbe, Tajikistan 4h 0m Somon Air
Erbil, Iraq 3h 5m flydubai
Esfahan, Iran 1h 45m Kish, IranAir
Faisalabad, Pakistan 3h 0m Pakistan
Glasgow, UK 8h 0m Emirates
Hyderabad, India 3h 25m Emirates, Air India, Jet Airways, …
Islamabad, Pakistan 3h 2m Emirates, Pakistan, Airblue, …
Jaipur, India 3h 20m Air-India Express
Jakarta, Indonesia 8h 15m Emirates, Garuda Indonesia, Yemenia
Jeddah Saudi Arabia 3h 4m Saudi Arabian, Emirates, nasair
Johannesburg, South Africa 8h 10m Emirates
Kabul, Afghanistan 2h 46m flydubai, Safi Airways Ltd., Kam Air, …
Kandahar, Afghanistan 2h 0m Ariana
Karachi, Pakistan 1h 57m Emirates, flydubai, Pakistan
Kharkiv, Ukraine 5h 15m flydubai
Khartoum, Sudan 4h 23m flydubai, Emirates, Sudan Airways
Kigali, Rwanda 5h 15m RwandAir
Lagos, Nigeria 8h 20m Emirates
Lahore, Pakistan 3h 0m Airblue, Emirates, Pakistan, …
Lamerd, Iran 1h 50m Iran Aseman
Lār, Iran 1h 0m Iran Aseman
Luanda, Angola 8h 16m Emirates, TAAG, Hainan
Manila, Philippines 8h 0m Emirates
Mashhad, Iran 2h 15m Iran Aseman
Mukalla, Yemen 2h 15m Yemenia, African Express
Multan, Pakistan 2h 50m Pakistan
Novosibirsk, Russia 5h 40m S7
Odesa, Ukraine 5h 5m AeroSvit
Peshawar, Pakistan 3h 3m Pakistan, Shaheen, Airblue, …
Port Sudan, Sudan 3h 40m flydubai
Quetta, Pakistan 2h 30m Pakistan
Riga, Latvia 6h 20m Air Baltic
Riyadh Saudi Arabia 1h 58m Saudi Arabian, Emirates, flydubai, …
Rostov, Russia 4h 20m Donavia
Sana'a, Yemen 2h 50m Emirates, Yemenia
Sao Paulo, Brazil 15h 15m Emirates
Shiraz, Iran 1h 30m Iran Aseman, IranAir
Sulaimania, Iraq 3h 10m flydubai
Tabrīz, Iran 2h 37m Caspian Airlines, Kish
Tashkent, Uzbekistan 3h 20m Uzbekistan
Tbilisi, Georgia 3h 20m flydubai, Georgian Airways
Tehran, Iran 2h 26m Emirates, Mahan, IranAir
Ufa, Russia 5h 0m flydubai
Yanbu Saudi Arabia 3h 20m flydubai
Yekaterinburg, Russia 5h 0m flydubai, Ural Airlines
Yerevan, Armenia 3h 15m Armavia, flydubai
Zāhedān, Iran 1h 30m Iran Aseman
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