I've tried to search for but didn't find anything exactly in the OGL rules about how poisons are handled. Are there any rules there?
In the D6 Adventure book on page 80 under Stamina (Physique) it goes into how to handle poisons.
To avoid the effects of a toxin (inhaled, ingested, or absorbed) or disease (encountered in any manner), a character makes a stamina roll. ( e first attempt after initial exposure does not count as an action; subsequent attempts to resist the toxin do.) Several factors figure into the difficulty of the attempt, including the deadliness and dosage of the poison in question. For example, a fatal bout of botulism has a difficulty of 9, while a killing dose of cyanide has a difficulty of 42.
This was the only entry directly I could find on it.
The excellent "REUP" core book has some poisoning rules. Under Miscellaneous Damage (p 102): 4D for Food Poisoning (very severe case) 8D+2 for General Poison (fatal dose)
And there are richer "optional rules" beginning on p 103. Excerpts:
the poisoner must make a Moderate first aid roll (or a Very Easy (A) medicine roll) as above. He must also make an alien species roll and check on the following table to establish the poison’s effectiveness
The victim takes one Wound every turn, until he has either taken the full damage or is dead
A Moderate (A) medicine or difficult first aid roll allows a person analyzing a poison to identify a specific type of poison
Once the poison is identified, the character may use the poison kit or the contents of a medpac to neutralize the poison (the difficulty of the skill roll is equal to the poison’s damage when using (A) medicine, and the damage +5 when using first aid)
There are also rules for Illness and Disease on the following page, which may be useful in similar situations.