I don't know the Olympus LS-P1, but you want to record in Linear PCM format as this is uncompressed and better quality than MP3. The bit rate determines the dynamic range (the bigger the number the greater the difference between the loudest and quietest thing you can record). The sampling rate has a impact on the max frequency of the sound you can record - this is 1/2 the sampling rate. As most birds vocalise below 10kHz, and field recordings normally suffer from ambient noise, CD quality (44.1kHz at 16 bit) is generally OK. However, if you have plenty of memory, you can select anything up from CD quality - on your device up to 96kHz 24 bit. It would be worth trialing higher quality setting, just to see whether you can detect any change in the recordings.
When recording, I would try selecting the manual gain option, rather that the 'presets' or auto level. You will then need to manually alter the gain so that the recording levels (as shown in the meters on the device screen during recording) are good, but not too high (you don't want the levels to go over and for clipping to occur as this ruins the recording). You may well find that with a bit of trial and error the gain level can be left at one setting - although of course if something pops up ultra close and blasts its head off, you are certainly going to have to change the recording level - assuming the standard setting you have adopted is for more distant and quieter sound.
Good luck!