Oklahoma requires a petition signed by 5% of the last vote cast (for the office at the top of the ballot) to get a newly-qualifying party on the ballot. The number of voters voting for President in Oklahoma declined in 2012, compared to 2008. Also, the presidential vote in 2008 was lower in Oklahoma than it had been in 2004. This is somewhat surprising, because Oklahoma is not losing population.
For 2014, the state requires 66,744 signatures. While this is overwhelmingly burdensome, it is easier than the 2010 requirement, which was 73,134.
Perhaps one reason Oklahoma voters have a low turnout in presidential elections is that they aren’t permitted to vote for anyone other than the Democratic and Republican nominees. For the last three elections in a row, no one can vote for President in Oklahoma without voting Democratic or Republican. No other state has a ballot access record in presidential years this bad, since the period 1956-1964.