OMG, been there done that! With both my kids, I was at my thinnest when they were about 9months, for the same reasons you mention (add in illness, food poisoning to my situation), and while I wasn't as thin as you (I'm 5'6", 118lbs at my lightest), I was thin enough to have people comment (e.g. "are you okay?" - which was the worst one of all!). I was also catching every little illness going around, since my immune system was so low (due to lack of sleep, primarily). I personally don't think introducing formula is the answer - there have been several studies (sorry don't have the references off-hand) that show "sleeping through the night" is not affected by feeding choices. In my entirely unscientific personal study of two children (both exclusively breastfed), one started sleeping through (6 hours +) around 3 months, the other still doesn't consistently sleep all night (at 13 months).
So, that said, this is what we did with the second: around 10 months, I started reading all the sleeping books at the library (No-Cry Sleep Solution is good) and I implemented a serious nighttime routine, which included putting Claire to bed earlier. Within a week of our new routine, she was going down & staying down much better (she usually wakes once/night). We tried having Dad get up w/ her and giving her a bottle of expressed milk - well she sucked about 4 oz down in a minute and a half and resumed screaming for me - not a roaring success, LOL! She wanted the comfort, not the food. So, I guess I'm saying you need to figure out a way to let the baby soothe himself back to sleep. Being the AP mommy I am, I jumped to go get Claire the minute she even whimpered...and at one point she was waking every hour and a half, just for a small suckle to put herself back to sleep (not a full meal). So, I started giving her the chance to get back to sleep on her own (e.g. looking at the clock and waiting a few minutes to see what happens - usually she goes back to sleep on her own). At first, this is hard - now I'm not saying CIO - if baby is CRYING, go get him, but if he's whimpering, etc, let it go a few minutes and then if it doesn't abate, perhaps send Dad in to pat his back, whatever baby likes. I think the first few nights of doing this may be harder than just feeding him, but he will soon find his own method of going back to sleep (like all adults do) and you will get some healthy rest.
Also, as far as solids go, Claire didn't really get going on them until 9 months (even though we tried starting at 6 months) because she didn't like purees! I kept giving her lovely organic home-made purees and she would gag! Well, she just really likes to chew - perhaps your little one is the same way??
As for you, I know it's hard to grab healthy stuff when the little ones need you, but perhaps try and make up some healthy snacks for yourself at night after the older ones are asleep (hubby can help here) so you can just grab them. Some ideas: hard-boiled eggs, pre-cut veggies & fruit in tupperware, hummus to go w/ pita bread or veggies, whole grain granola bars, yogurt, rotisserie chicken already pulled apart and stored in bags ready to go onto salads made from pre-washed spinach.. Make sure you get plenty of protein!! Good luck!