How long does it take to get out of an overuse of migraine medication? 

Triptans 

Taking a dose of triptan, it takes between 2 hours for Imigran and Maxalt and 6 hours for Naragran before half of the active substance is excreted from the body (1). It's called half-life. 

After twice as long as half-life, there is only 1/4 of the active substance left in the body. And after 3 times the half-life 1/8 is left. Theoretically, there will always be a tiny bit of the active substance in the body, ie. after around 8 half-lives (ie 2 to 3 days) the amount of active drug is reduced to 1/256th. There are no studies showing that these tiny amounts of triptan has any effect in the body. One can therefore expect to be out of triptan effect in less than a week. 

OTC Medicine 

Taking a dose of painkillers over the counter medication such as aspirin or paracetamol, the effect is quite different. 

Aspirin

Aspirin is excreted through the kidneys and has a half life in the body around 3 hours (2) at normal doses and up to 30 hours at very high doses (3). Aspirin influences blood platelets so they do not clump together because aspirin inhibits the action of the enzyme COX. COX is is released from the storage vesicles in the platelets when aspirin is in the blood. COX is a pain inhibitor, and this is the way aspirin works. Since platelets do not clump so much when you take aspirin, it is also used against blood clots. 

Large doses of aspirin also inhibits the formation of prostaglandin I2, which causes blood vessels to dilate, ie. Aspirin counters the dilation of blood vessels during the the pain phase in migraine. Finally, aspirin is an excellent remedy for inflammation. Although aspirin is excreted from the body in relatively few hours, it leaves some of platelets in a condition which can not be restored to normal, as their COX supply is used up. 

The body is therefore not entirely free of  the influence of aspirin  for a month or two, until a new generation of platelets is formed. Although the active ingredient is out of the body, there is a residual effect that lasts several weeks. 

A large dose of aspirin provides 'ringing in the ears' or tinnitus symptoms. If you experience this ringing in the ears, there is good reason to reduce your consumption of aspirin. 

Paracetamol 

Paracetamol is metabolized in the liver, and half of the drug is excreted after approximately 2 hours. It means that the body quickly (within a few days) is free from the effect of paracetamol. 

Paracetamol should never be taken in large quantities. Most of the material is degraded in the liver and excreted quickly, but around  5% is converted to benzoquinoneimin. This agent connects with the compound glutathione also found in the liver, until there is no more of this in the liver. Additional benzoquinoneimin then attacks proteins in the liver and provides liver damage. It takes 3 to 4 days to deplete hepatic stores of glutathione. 

The damage occurs when taking 150 mg / kg bodyweight (approximately 7.5 g for a 50 kg person) paracetamol within a short time. Treatment should ideally start within 12 hours after overdose to have an effect (4). Unfortunately you do not feel any symptoms of the upcoming poisoning during the first 24 hours. 

(1). S. S. Jhee, T. Shiovitz, A. W. Crawford and N. R. Cutler, 2001. Pharmacokinetics and pharmacodynamics of the triptan antimigraine agents: a comparative review. Clin Pharmacokinet. 40, 189-205. 

(2) G.  Levy, 1965 J. Pharm. Sci., 54, 959 

(3) http://www.migraines.org/treatment/proasprn.htm