Why are the higher alkanes more toxic?
It relates to their increasing affinity for accumulation in body fats.
As the human body contains a large amount of water, and because hydrophobicity increases with chain length, higher alkanes are increasingly incompatible with water. Therefore when ingested they tend to preferentially be stored in the fat cells in our bodies.
Hydrophilic (polar) substances can be filtered out by our kidneys and excreted in urine, but there is no mechanism to remove non-polar hydrophobic impurities from fat. That means it simply accumulates, and eventually reaches a level whereby toxicity becomes an issue.
Note that lower alkanes such as ethane may well be dangerous in that you can asphyxiate if concentrations are very high, but toxicity specifically relates to the ability to cause damage to organisms. You can asphxiate in water (i.e. drowing) but that doesn't mean that water is toxic.