From a 1995 article from the Journal of Applied Bacteriology:

Tea tree oil, or the essential oil of Melaleuca alternifolia, is becoming increasingly popular as a naturally occurring antimicrobial agent.

The antimicrobial activity of eight components of tea tree oil were evaluated:

1. 1,8-cineole
   
2. 1-terpinen-4-ol - Terpinen-4-ol was active against all the test organisms
3. rho-cymene - rho-cymene demonstrated no antimicrobial activity
4. linalool - Linalool was active against all organisms with the exception of Pseudomonas aeruginosa.
5. alpha-terpinene
   
6. gamma-terpinene
   
7. alpha-terpineol - alpha-terpineol was active against all organisms with the exception of Pseudomonas aeruginosa.
8. terpinolene

• Carson CF et al. Antimicrobial activity of the major components of the essential oil of Melaleuca alternifolia. J Appl Bacteriol. 1995 Mar;78(3):264-9.

From a 1995 article from the Journal of Antimicrobial Chemotherapy:

66 isolates of Staphylococcus aureus tested were susceptible to the essential oil of Melaleuca alternifolia, or tea tree oil. Of the isolates tested, 64 were methicillin-resistant S. aureus (MRSA) and 33 were mupirocin-resistant.

• Carson CF et al. Susceptibility of methicillin-resistant Staphylococcus aureus to the essential oil of Melaleuca alternifolia. J Antimicrob Chemother. 1995 Mar;35(3):421-4.

What is the mode of antimicrobial action of the essential oil of Melaleuca alternifolia (tea tree oil)?

The ability of tea tree oil to disrupt the permeability barrier of cell membrane structures and the accompanying loss of chemiosmotic control is the most likely source of its lethal action.

• Cox SD et al. The mode of antimicrobial action of the essential oil of Melaleuca alternifolia (tea tree oil). J Appl Microbiol. 2000 Jan;88(1):170-5.

Can tea tree oil treat a toenail fungal infection?

The prevalence of onychomycosis, a superficial fungal infection that destroys the entire nail unit, is rising, with no satisfactory cure.
A randomized, double-blind, placebo-controlled study was done to examine the clinical efficacy and tolerability of 2% butenafine hydrochloride and 5% Melaleuca alternifolia oil incorporated in a cream to manage toenail onychomycosis.
After 16 weeks, 80% of patients using medicated cream were cured, as opposed to none in the placebo group.

• Syed TA et al. Treatment of toenail onychomycosis with 2% butenafine and 5% Melaleuca alternifolia (tea tree) oil in cream. Trop Med Int Health. 1999 Apr;4(4):284-7.